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Models and integral differentials of hyperelliptic curves Glasg. Math. J. (IF 0.5) Pub Date : 2024-03-18 Simone Muselli
Let $C\; : \;y^2=f(x)$ be a hyperelliptic curve of genus $g\geq 1$ , defined over a complete discretely valued field $K$ , with ring of integers $O_K$ . Under certain conditions on $C$ , mild when residue characteristic is not $2$ , we explicitly construct the minimal regular model with normal crossings $\mathcal{C}/O_K$ of $C$ . In the same setting we determine a basis of integral differentials of
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Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity Glasg. Math. J. (IF 0.5) Pub Date : 2024-03-11 Qizheng You, Jiawen Zhang
In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s $4$ -point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.
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A Helfrich functional for compact surfaces in Glasg. Math. J. (IF 0.5) Pub Date : 2024-02-26 Zhongwei Yao
Let $f\;:\; M\rightarrow \mathbb{C}P^{2}$ be an isometric immersion of a compact surface in the complex projective plane $\mathbb{C}P^{2}$ . In this paper, we consider the Helfrich-type functional $\mathcal{H}_{\lambda _{1},\lambda _{2}}(f)=\int _{M}(|H|^{2}+\lambda _{1}+\lambda _{2} C^{2})\textrm{d} M$ , where $\lambda _{1}, \lambda _{2}\in \mathbb{R}$ with $\lambda _{1}\geqslant 0$ , $H$ and $C$
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On twisted group ring isomorphism problem for p-groups Glasg. Math. J. (IF 0.5) Pub Date : 2024-02-16 Gurleen Kaur, Surinder Kaur, Pooja Singla
In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$ -groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently examined by Margolis-Schnabel. Our focus lies on a specific invariant, referred to as the generalized corank, which relates to the twisted complex group algebra isomorphism
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Abelian absolute Galois groups Glasg. Math. J. (IF 0.5) Pub Date : 2024-02-02 Moshe Jarden
Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if $K$ is a finitely generated extension of transcendence degree $r$ of a global field and $A$ is a closed abelian subgroup of $\textrm{Gal}(K)$ , then ${\mathrm{rank}}(A)\le r+1$ . Moreover, if $\mathrm{char}(K)=0$ , then ${\hat{\mathbb{Z}}}^{r+1}$ is isomorphic to a closed subgroup of $\textrm{Gal}(K)$ .
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Kato’s main conjecture for potentially ordinary primes Glasg. Math. J. (IF 0.5) Pub Date : 2024-01-26 Katharina Müller
In this paper, we prove Kato’s main conjecture for $CM$ modular forms for primes of potentially ordinary reduction under certain hypotheses on the modular form.
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Leopoldt-type theorems for non-abelian extensions of Glasg. Math. J. (IF 0.5) Pub Date : 2024-01-25 Fabio Ferri
We prove new results concerning the additive Galois module structure of wildly ramified non-abelian extensions $K/\mathbb{Q}$ with Galois group isomorphic to $A_4$ , $S_4$ , $A_5$ , and dihedral groups of order $2p^n$ for certain prime powers $p^n$ . In particular, when $K/\mathbb{Q}$ is a Galois extension with Galois group $G$ isomorphic to $A_4$ , $S_4$ or $A_5$ , we give necessary and sufficient
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Classifying spaces for families of abelian subgroups of braid groups, RAAGs and graphs of abelian groups Glasg. Math. J. (IF 0.5) Pub Date : 2024-01-11 Porfirio L. León Álvarez
Given a group $G$ and an integer $n\geq 0$ , we consider the family ${\mathcal F}_n$ of all virtually abelian subgroups of $G$ of $\textrm{rank}$ at most $n$ . In this article, we prove that for each $n\ge 2$ the Bredon cohomology, with respect to the family ${\mathcal F}_n$ , of a free abelian group with $\textrm{rank}$ $k \gt n$ is nontrivial in dimension $k+n$ ; this answers a question of Corob
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Dehn functions of mapping tori of right-angled Artin groups Glasg. Math. J. (IF 0.5) Pub Date : 2024-01-11 Kristen Pueschel, Timothy Riley
The algebraic mapping torus $M_{\Phi }$ of a group $G$ with an automorphism $\Phi$ is the HNN-extension of $G$ in which conjugation by the stable letter performs $\Phi$ . We classify the Dehn functions of $M_{\Phi }$ in terms of $\Phi$ for a number of right-angled Artin groups (RAAGs) $G$ , including all $3$ -generator RAAGs and $F_k \times F_l$ for all $k,l \geq 2$ .
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On a variant of the product replacement algorithm Glasg. Math. J. (IF 0.5) Pub Date : 2024-01-09 C.R. Leedham-Green
We discuss a variant, named ‘Rattle’, of the product replacement algorithm. Rattle is a Markov chain, that returns a random element of a black box group. The limiting distribution of the element returned is the uniform distribution. We prove that, if the generating sequence is long enough, the probability distribution of the element returned converges unexpectedly quickly to the uniform distribution
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Unitary groups, -theory, and traces Glasg. Math. J. (IF 0.5) Pub Date : 2023-12-15 Pawel Sarkowicz
We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$ -theoretic regularity conditions, these maps can be seen to commute with the pairing between $K_0$ and traces. If the homomorphism is contractive and sends the unit circle to the unit circle, the map
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The connective Glasg. Math. J. (IF 0.5) Pub Date : 2023-12-11 Donald M. Davis, W. Stephen Wilson
We compute $ku^*\left(K\!\left({\mathbb{Z}}_p,2\right)\right)$ and $ku_*\left(K\!\left({\mathbb{Z}}_p,2\right)\right)$, the connective $KU$-cohomology and connective $KU$-homology groups of the mod-$p$ Eilenberg–MacLane space $K\!\left({\mathbb{Z}}_p,2\right)$, using the Adams spectral sequence. We obtain a striking interaction between $h_0$-extensions and exotic extensions. The mod-$p$ connective
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A note on almost Yamabe solitons Glasg. Math. J. (IF 0.5) Pub Date : 2023-11-29 Wagner Oliveira Costa-Filho
In this paper, we present a sufficient condition for almost Yamabe solitons to have constant scalar curvature. Additionally, under some geometric scenarios, we provide some triviality and rigidity results for these structures.
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On -unramified extensions over imaginary quadratic fields Glasg. Math. J. (IF 0.5) Pub Date : 2023-11-29 Kwang-Seob Kim, Joachim König
Let $n$ be an integer congruent to $0$ or $3$ modulo $4$. Under the assumption of the ABC conjecture, we prove that, given any integer $m$ fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group $A_n \times C_m$. The same result is obtained unconditionally in special cases.
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A classification of some thick subcategories in locally noetherian Grothendieck categories Glasg. Math. J. (IF 0.5) Pub Date : 2023-11-23 Kaili Wu, Xinchao Ma
Let $\mathcal{A}$ be a locally noetherian Grothendieck category. We classify all full subcategories of $\mathcal{A}$ which are thick and closed under taking arbitrary direct sums and injective envelopes by injective spectrum. This result gives a generalization from the commutative noetherian ring to the locally noetherian Grothendieck category.
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A natural pseudometric on homotopy groups of metric spaces Glasg. Math. J. (IF 0.5) Pub Date : 2023-11-08 Jeremy Brazas, Paul Fabel
For a path-connected metric space $(X,d)$, the $n$-th homotopy group $\pi _n(X)$ inherits a natural pseudometric from the $n$-th iterated loop space with the uniform metric. This pseudometric gives $\pi _n(X)$ the structure of a topological group, and when $X$ is compact, the induced pseudometric topology is independent of the metric $d$. In this paper, we study the properties of this pseudometric
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Tropical invariants for binary quintics and reduction types of Picard curves Glasg. Math. J. (IF 0.5) Pub Date : 2023-11-06 Paul Alexander Helminck, Yassine El Maazouz, Enis Kaya
In this paper, we express the reduction types of Picard curves in terms of tropical invariants associated with binary quintics. We also give a general framework for tropical invariants associated with group actions on arbitrary varieties. The problem of finding tropical invariants for binary forms fits in this general framework by mapping the space of binary forms to symmetrized versions of the Deligne–Mumford
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Notes on hyperelliptic mapping class groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-31 Marco Boggi
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural epimorphisms between mapping class groups of surfaces with marked points. We study these groups in a systematic way. An application of this theory is a counterexample to the
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On the reducing projective dimension over local rings Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-31 Olgur Celikbas, Souvik Dey, Toshinori Kobayashi, Hiroki Matsui
In this paper, we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya–Celikbas and Araya–Takahashi. We raise the question whether the residue field of each commutative Noetherian local ring has finite reducing projective dimension and obtain an affirmative answer for the question for a large class of local rings. Furthermore
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Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-27 Brad Rodgers, Harshith Sai Vallabhaneni
We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble, as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble. Both moments and ratios are studied via symmetric function theory and a general formula
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Representatives of similarity classes of matrices over PIDs corresponding to ideal classes Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-18 Lucy Knight, Alexander Stasinski
For a principal ideal domain $A$, the Latimer–MacDuffee correspondence sets up a bijection between the similarity classes of matrices in $\textrm{M}_{n}(A)$ with irreducible characteristic polynomial $f(x)$ and the ideal classes of the order $A[x]/(f(x))$. We prove that when $A[x]/(f(x))$ is maximal (i.e. integrally closed, i.e. a Dedekind domain), then every similarity class contains a representative
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Quantum symmetries of Cayley graphs of abelian groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-12 Daniel Gromada
We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of the halved cube graph, the folded cube graph, and the Hamming graphs.
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Mutating signed -exceptional sequences Glasg. Math. J. (IF 0.5) Pub Date : 2023-10-12 Aslak Bakke Buan, Bethany Rose Marsh
We establish some properties of $\tau$ -exceptional sequences for finite-dimensional algebras. In an earlier paper, we established a bijection between the set of ordered support $\tau$ -tilting modules and the set of complete signed $\tau$ -exceptional sequences. We describe the action of the symmetric group on the latter induced by its natural action on the former. Similarly, we describe the effect
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Null hypersurfaces in 4-manifolds endowed with a product structure Glasg. Math. J. (IF 0.5) Pub Date : 2023-09-28 Nikos Georgiou
In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces that are null with respect to this neutral metric, and in particular we study their geometric properties with respect to the Einstein metric. Firstly, we show that
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Relative Dehn functions, hyperbolically embedded subgroups and combination theorems Glasg. Math. J. (IF 0.5) Pub Date : 2023-08-25 Hadi Bigdely, Eduardo Martínez-Pedroza
Consider the following classes of pairs consisting of a group and a finite collection of subgroups: • $ \mathcal{C}= \left \{ (G,\mathcal{H}) \mid \text{$\mathcal{H}$ is hyperbolically embedded in $G$} \right \}$ • $ \mathcal{D}= \left \{ (G,\mathcal{H}) \mid \text{the relative Dehn function of $(G,\mathcal{H})$ is well-defined} \right \} .$ Let $G$ be a group that splits as a finite graph of groups
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On the Jones polynomial modulo primes Glasg. Math. J. (IF 0.5) Pub Date : 2023-08-15 Valeriano Aiello, Sebastian Baader, Livio Ferretti
We derive an upper bound on the density of Jones polynomials of knots modulo a prime number $p$, within a sufficiently large degree range: $4/p^7$. As an application, we classify knot Jones polynomials modulo two of span up to eight.
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On the structure of lower bounded HNN extensions Glasg. Math. J. (IF 0.5) Pub Date : 2023-08-10 Paul Bennett, Tatiana B. Jajcayová
This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if $S^* = [ S;\; U_1,U_2;\; \phi ]$ is a lower bounded HNN extension then the maximal subgroups of $S^*$ may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the $\mathcal{D}$-classes of
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A symmetry of silting quivers Glasg. Math. J. (IF 0.5) Pub Date : 2023-07-26 Takuma Aihara, Qi Wang
We investigate symmetry of the silting quiver of a given algebra which is induced by an anti-automorphism of the algebra. In particular, one shows that if there is a primitive idempotent fixed by the anti-automorphism, then the 2-silting quiver ($=$ the support $\tau$-tilting quiver) has a bisection. Consequently, in that case, we obtain that the cardinality of the 2-silting quiver is an even number
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Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2 Glasg. Math. J. (IF 0.5) Pub Date : 2023-07-25 Abel Castorena, Juan Bosco Frías-Medina
In this work, we study the Humbert-Edge curves of type 5, defined as a complete intersection of four diagonal quadrics in ${\mathbb{P}}^5$. We characterize them using Kummer surfaces, and using the geometry of these surfaces, we construct some vanishing thetanulls on such curves. In addition, we describe an argument to give an isomorphism between the moduli space of Humbert-Edge curves of type 5 and
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A presentation for the Eisenstein-Picard modular group in three complex dimensions Glasg. Math. J. (IF 0.5) Pub Date : 2023-07-25 Jieyan Wang, Baohua Xie
A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.
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Generalized tilting theory in functor categories Glasg. Math. J. (IF 0.5) Pub Date : 2023-07-10 Xi Tang
This paper is devoted to the study of generalized tilting theory of functor categories in different levels. First, we extend Miyashita’s proof (Math Z 193:113–146,1986) of the generalized Brenner–Butler theorem to arbitrary functor categories $\mathop{\textrm{Mod}}\nolimits\!(\mathcal{C})$ with $\mathcal{C}$ an annuli variety. Second, a hereditary and complete cotorsion pair generated by a generalized
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Subrepresentations in the homology of finite covers of graphs Glasg. Math. J. (IF 0.5) Pub Date : 2023-07-06 Xenia Flamm
Let $p \;:\; Y \to X$ be a finite, regular cover of finite graphs with associated deck group $G$, and consider the first homology $H_1(Y;\;{\mathbb{C}})$ of the cover as a $G$-representation. The main contribution of this article is to broaden the correspondence and dictionary between the representation theory of the deck group $G$ on the one hand and topological properties of homology classes in
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Continuously many quasi-isometry classes of residually finite groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-06-19 Hip Kuen Chong, Daniel T. Wise
We study a family of finitely generated residually finite small-cancellation groups. These groups are quotients of $F_2$ depending on a subset $S$ of positive integers. Varying $S$ yields continuously many groups up to quasi-isometry.
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A note on virtual duality and automorphism groups of right-angled Artin groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-06-19 Richard D. Wade, Benjamin Brück
A theorem of Brady and Meier states that a right-angled Artin group is a duality group if and only if the flag complex of the defining graph is Cohen–Macaulay. We use this to give an example of a RAAG with the property that its outer automorphism group is not a virtual duality group. This gives a partial answer to a question of Vogtmann. In an appendix, Brück describes how he used a computer-assisted
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Cohomology in singular blocks of parabolic category Glasg. Math. J. (IF 0.5) Pub Date : 2023-05-15 Jonathan Gruber
We determine the dimensions of $\textrm{Ext}$-groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category $\mathcal{O}$ for complex semisimple Lie algebras and affine Kac-Moody algebras.
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Detecting and describing ramification for structured ring spectra Glasg. Math. J. (IF 0.5) Pub Date : 2023-04-24 Eva Höning, Birgit Richter
John Rognes developed a notion of Galois extension of commutative ring spectra, and this includes a criterion for identifying an extension as unramified. Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological André–Quillen homology. In the classical algebraic context, it is important to distinguish between tame and wild ramification
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Division algebras and MRD codes from skew polynomials Glasg. Math. J. (IF 0.5) Pub Date : 2023-04-20 D. Thompson, S. Pumplün
Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\;\sigma,\delta ]$ a skew polynomial ring. Using skew polynomials $f\in R$ , we construct division algebras and maximum rank distance codes consisting of matrices with entries in a noncommutative division algebra or field. These include Jha Johnson semifields, and the classes of classical and twisted Gabidulin codes constructed
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KMS states on Glasg. Math. J. (IF 0.5) Pub Date : 2023-04-03 Anbu Arjunan, Sruthymurali, S. Sundar
Let $C_c^{*}(\mathbb{N}^{2})$ be the universal $C^{*}$-algebra generated by a semigroup of isometries $\{v_{(m,n)}\,:\, m,n \in \mathbb{N}\}$ whose range projections commute. We analyse the structure of KMS states on $C_{c}^{*}(\mathbb{N}^2)$ for the time evolution determined by a homomorphism $c\,:\,\mathbb{Z}^{2} \to \mathbb{R}$. In contrast to the reduced version $C_{red}^{*}(\mathbb{N}^{2})$, we
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A note on grid homology in lens spaces: coefficients and computations Glasg. Math. J. (IF 0.5) Pub Date : 2023-03-31 Daniele Celoria
We present a combinatorial proof for the existence of the sign-refined grid homology in lens spaces and a self-contained proof that $\partial _{\mathbb{Z}}^2 = 0$ . We also present a Sage programme that computes $\widehat{\mathrm{GH}} (L(p,q),K;\mathbb{Z})$ and provide empirical evidence supporting the absence of torsion in these groups.
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Finite image homomorphisms of the braid group and its generalizations Glasg. Math. J. (IF 0.5) Pub Date : 2023-03-23 Nancy Scherich, Yvon Verberne
Using totally symmetric sets, Chudnovsky–Kordek–Li–Partin gave a superexponential lower bound on the cardinality of non-abelian finite quotients of the braid group. In this paper, we develop new techniques using multiple totally symmetric sets to count elements in non-abelian finite quotients of the braid group. Using these techniques, we improve the lower bound found by Chudnovsky et al. We exhibit
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Hausdorff dimension of sets defined by almost convergent binary expansion sequences Glasg. Math. J. (IF 0.5) Pub Date : 2023-03-13 Qing-Yao Song
In this paper, we study the Hausdorff dimension of sets defined by almost convergent binary expansion sequences. More precisely, the Hausdorff dimension of the following set \begin{align*} \bigg\{x\in[0,1)\;:\;\frac{1}{n}\sum_{k=a}^{a+n-1}x_{k}\longrightarrow\alpha\textrm{ uniformly in }a\in\mathbb{N}\textrm{ as }n\rightarrow\infty\bigg\} \end{align*} is determined for any $ \alpha\in[0,1] $ . This
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Some characterizations of expanding and steady Ricci solitons Glasg. Math. J. (IF 0.5) Pub Date : 2023-03-13 Márcio S. Santos
In this short note, we deal with complete noncompact expanding and steady Ricci solitons of dimension $n\geq 3.$ More precisely, under an integrability assumption, we obtain a characterization for the generalized cigar Ricci soliton and the Gaussian Ricci soliton.
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Gaps between prime divisors and analogues in Diophantine geometry Glasg. Math. J. (IF 0.5) Pub Date : 2023-02-27 Efthymios Sofos
Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotics for all moments. Furthermore, we prove a generalisation stating that the gaps between primes p for which there is no $\mathbb{Q}_p$ -point on a random variety are Poisson distributed.
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On the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces Glasg. Math. J. (IF 0.5) Pub Date : 2023-02-02 O. Mata-Gutiérrez, L. Roa-Leguizamón, H. Torres-López
The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let X be a nonsingular irreducible complex surface, and let E be a vector bundle of rank n on X. We use the m-elementary transformation of E at a point $x \in X$ to show that there exists an embedding from the Grassmannian variety
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Conjugacy growth in the higher Heisenberg groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-01-23 Alex Evetts
We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics are stable when passing to commensurable groups, by understanding their twisted conjugacy growth. We also use these estimates to prove that, in certain cases,
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Slope equality of non-hyperelliptic Eisenbud–Harris special fibrations of genus 4 Glasg. Math. J. (IF 0.5) Pub Date : 2023-01-20 Makoto Enokizono
The Horikawa index and the local signature are introduced for relatively minimal fibered surfaces whose general fiber is a non-hyperelliptic curve of genus 4 with unique trigonal structure.
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On parabolic subgroups of symplectic reflection groups Glasg. Math. J. (IF 0.5) Pub Date : 2023-01-10 Gwyn Bellamy, Johannes Schmitt, Ulrich Thiel
Using Cohen’s classification of symplectic reflection groups, we prove that the parabolic subgroups, that is, stabilizer subgroups, of a finite symplectic reflection group, are themselves symplectic reflection groups. This is the symplectic analog of Steinberg’s Theorem for complex reflection groups. Using computational results required in the proof, we show the nonexistence of symplectic resolutions
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Geometric filling curves on punctured surfaces Glasg. Math. J. (IF 0.5) Pub Date : 2022-12-15 Nhat Minh Doan
This paper is about a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly truncated orthogeodesic that are $\varepsilon$ -dense on a given compact set on the surface.
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Galois representations of superelliptic curves Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-24 Ariel Pacetti, Angel Villanueva
A superelliptic curve over a discrete valuation ring $\mathscr{O}$ of residual characteristic p is a curve given by an equation $\mathscr{C}\;:\; y^n=\,f(x)$ , with $\textrm{Disc}(\,f)\neq 0$ . The purpose of this article is to describe the Galois representation attached to such a curve under the hypothesis that f(x) has all its roots in the fraction field of $\mathscr{O}$ and that $p \nmid n$ . Our
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Double relative commutants in coronas of separable C*-algebras Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-23 Dan Kučerovský, Martin Mathieu
We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen in 1988. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu later proved a C*-algebraic double commutant theorem for subalgebras of the Calkin algebra
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Yet another Freiheitssatz: Mating finite groups with locally indicable ones Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-14 Anton A. Klyachko, Mikhail A. Mikheenko
The main result includes as special cases on the one hand, the Gerstenhaber–Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, the Brodskii–Howie–Short theorem (1980–1984) generalising Magnus’s Freiheitssatz (1930).
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On canonical Fano intrinsic quadrics Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-07 Christoff Hische
We classify all $\mathbb{Q}$ -factorial Fano intrinsic quadrics of dimension three and Picard number one having at most canonical singularities.
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A characterization of potent rings Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-02 Greg Oman
An associative ring R is called potent provided that for every $x\in R$ , there is an integer $n(x)>1$ such that $x^{n(x)}=x$ . A celebrated result of N. Jacobson is that every potent ring is commutative. In this note, we show that a ring R is potent if and only if every nonzero subring S of R contains a nonzero idempotent. We use this result to give a generalization of a recent result of Anderson
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harmonic 1-forms on hypersurfaces with finite index Glasg. Math. J. (IF 0.5) Pub Date : 2022-11-02 Xiaoli Chao, Bin Shen, Miaomiao Zhang
In the present note, we establish a finiteness theorem for $L^p$ harmonic 1-forms on hypersurfaces with finite index, which is an extension of the result of Choi and Seo (J. Geom. Phys.129 (2018), 125–132).
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Null, recursively starlike-equivalent decompositions shrink Glasg. Math. J. (IF 0.5) Pub Date : 2022-10-28 Jeffrey Meier, Patrick Orson, Arunima Ray
A subset E of a metric space X is said to be starlike-equivalent if it has a neighbourhood which is mapped homeomorphically into $\mathbb{R}^n$ for some n, sending E to a starlike set. A subset $E\subset X$ is said to be recursively starlike-equivalent if it can be expressed as a finite nested union of closed subsets $\{E_i\}_{i=0}^{N+1}$ such that $E_{i}/E_{i+1}\subset X/E_{i+1}$ is starlike-equivalent
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Polyhedral groups in Glasg. Math. J. (IF 0.5) Pub Date : 2022-08-11 Vincent Knibbeler, Sara Lombardo, Casper Oelen
We classify embeddings of the finite groups $A_4$ , $S_4$ and $A_5$ in the Lie group $G_2(\mathbb C)$ up to conjugation.
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On the moments of characteristic polynomials Glasg. Math. J. (IF 0.5) Pub Date : 2022-08-05 Bhargavi Jonnadula, Jonathan P. Keating, Francesco Mezzadri
We calculate the moments of the characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, at a position t in the bulk of the spectrum, as a series expansion in powers of t. We focus in particular on the Gaussian Unitary Ensemble. We employ a novel approach to calculate the coefficients in this series expansion of the moments, appropriately scaled
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An extension of the van Hemmen–Ando norm inequality Glasg. Math. J. (IF 0.5) Pub Date : 2022-08-03 Hamed Najafi
Let $C_{\||.\||}$ be an ideal of compact operators with symmetric norm $\||.\||$ . In this paper, we extend the van Hemmen–Ando norm inequality for arbitrary bounded operators as follows: if f is an operator monotone function on $[0,\infty)$ and S and T are bounded operators in $\mathbb{B}(\mathscr{H}\;\,)$ such that ${\rm{sp}}(S),{\rm{sp}}(T) \subseteq \Gamma_a=\{z\in \mathbb{C} \ | \ {\rm{re}}(z)\geq
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Maximal order Abelian subgroups of Coxeter groups Glasg. Math. J. (IF 0.5) Pub Date : 2022-08-02 John M. Burns, Goetz Pfeiffer
In this note, we give a classification of the maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analog of Cartan’s theorem that all maximal tori in a connected compact Lie group are conjugate.
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Automorphism groups of endomorphisms of Glasg. Math. J. (IF 0.5) Pub Date : 2022-07-13 Julia Cai, Benjamin Hutz, Leo Mayer, Max Weinreich
For any algebraically closed field K and any endomorphism f of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of f are the Möbius transformations that commute with f, and these form a finite subgroup of $\operatorname{PGL}_2(K)$ . In the moduli space of complex dynamical systems, the locus of maps with nontrivial automorphisms has been studied in detail and there are techniques for constructing