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  • On the moduli spaces of singular principal bundles on stable curves
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Ángel Luis Muñoz Castañeda

    We prove the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of δ-(semi)stable singular principal G-bundles over families of reduced projective and connected nodal curves, and to reduce the construction of the universal moduli space over 𝓜g to the construction of the universal moduli space of

    更新日期:2020-10-20
  • Differentiability of projective transformations in dimension 2
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Julius Lang

    It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [] for dimension three and higher from 1965.

    更新日期:2020-10-08
  • Tropical superelliptic curves
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Madeline Brandt; Paul Alexander Helminck

    We present an algorithm for computing the Berkovich skeleton of a superelliptic curve yn = f(x) over a valued field. After defining superelliptic weighted metric graphs, we show that each one is realizable by an algebraic superelliptic curve when n is prime. Lastly, we study the locus of superelliptic weighted metric graphs inside the moduli space of tropical curves of genus g.

    更新日期:2020-10-08
  • Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Mario Maican

    We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description:

    更新日期:2020-10-08
  • Explicit computation of some families of Hurwitz numbers, II
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Carlo Petronio

    We continue our computation, using a combinatorial method based on Gronthendieck’s dessins d’enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate on data with the surface of genus g as source surface, the sphere as target surface, 3 branching points, degree 2k, and local degrees over the branching points of

    更新日期:2020-10-08
  • New dense superball packings in three dimensions
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08
    Maria Dostert; Frank Vallentin

    We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l3p norm) with p ∈ (1, 1.58]. We conjecture that the family also exists for p ∈ (1.58, log2 3 = 1.5849625…]. Like in the densest lattice packing of regular octahedra, each superball in our family of lattice packings has 14 neighbors.

    更新日期:2020-10-08
  • Frontmatter
    Adv. Geom. (IF 0.736) Pub Date : 2020-10-08

    Journal Name: Advances in Geometry Volume: 20 Issue: 4 Pages: i-iii

    更新日期:2020-10-08
  • Geodesic orbit Randers metrics on spheres
    Adv. Geom. (IF 0.736) Pub Date : 2020-09-22
    Shaoxiang Zhang; Zaili Yan

    Studying geodesic orbit Randers metrics on spheres, we obtain a complete classification of such metrics. Our method relies upon the classification of geodesic orbit Riemannian metrics on the spheres Sn in [] and the navigation data in Finsler geometry. We also construct some explicit U(n + 1)-invariant metrics on S2n+1 and Sp(n + 1)U(1)-invariant metrics on S4n+3.

    更新日期:2020-09-22
  • On vector bundles over reducible curves with a node
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-26
    Filippo F. Favale; Sonia Brivio

    Let C be a curve with two smooth components and a single node, and let 𝓤C(w, r, χ) be the moduli space of w-semistable classes of depth one sheaves on C having rank r on both components and Euler characteristic χ. In this paper, under suitable assumptions, we produce a projective bundle over the product of the moduli spaces of semistable vector bundles of rank r on each component and we show that

    更新日期:2020-07-26
  • The geometry of H4 polytopes
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-05
    Tomme Denney; Da’Shay Hooker; De’Janeke Johnson; Tianna Robinson; Majid Butler; Sandernisha Claiborne

    We describe the geometry of an arrangement of 24-cells inscribed in the 600-cell. In we apply our results to the even unimodular lattice E8 and show how the 600-cell transforms E8/2E8, an 8-space over the field F2, into a 4-space over F4 whose points, lines and planes are labeled by the geometric objects of the 600-cell.

    更新日期:2020-07-06
  • Homogeneous Finsler spaces with exponential metric
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-05
    Gauree Shanker; Kirandeep Kaur

    We prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

    更新日期:2020-07-06
  • Uniform modular lattices and affine buildings
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-05
    Hiroshi Hirai

    A simple lattice-theoretic characterization for affine buildings of type A is obtained. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and affine buildings of type A constitute the same object. This is an affine counterpart of the well-known equivalence between projective geometries (≃ complemented modular lattices) and spherical buildings

    更新日期:2020-07-06
  • Frontmatter
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-05

    Journal Name: Advances in Geometry Volume: 20 Issue: 3 Pages: i-iii

    更新日期:2020-07-06
  • Solutions to the affine quasi-Einstein equation for homogeneous surfaces
    Adv. Geom. (IF 0.736) Pub Date : 2020-07-05
    M. Brozos-Vázquez; E. García-Río; P. Gilkey; X. Valle-Regueiro

    We examine the space of solutions to the affine quasi–Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitons, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. We use the dimension of the space of affine Killing

    更新日期:2020-07-05
  • Building lattices and zeta functions
    Adv. Geom. (IF 0.736) Pub Date : 2020-04-28
    Anton Deitmar; Ming-Hsuan Kang; Rupert McCallum

    We give a Lefschetz formula for tree lattices and apply it to geometric zeta functions. We further generalize Bass’s approach to Ihara zeta functions to the higher-dimensional case of a building.

    更新日期:2020-04-28
  • The degree of the tangent and secant variety to a projective surface
    Adv. Geom. (IF 0.736) Pub Date : 2020-04-28
    Andrea Cattaneo

    We present a way of computing the degree of the secant (resp. tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is 3-very ample. This method exploits the link between these varieties and the Hilbert scheme 0-dimensional subschemes of length 2 of the surface.

    更新日期:2020-04-28
  • Additive structures on f-vector sets of polytopes
    Adv. Geom. (IF 0.736) Pub Date : 2020-04-28
    Günter M. Ziegler

    We show that the f-vector sets of d-polytopes have non-trivial additive structure: They span affine lattices and are embedded in monoids that we describe explicitly. Moreover, for many large subclasses, such as the simple polytopes, or the simplicial polytopes, there are monoid structures on the set of f-vectors by themselves: “addition of f-vectors minus the f-vector of the d-simplex” always yields

    更新日期:2020-04-28
  • Higher algebraic structures in Hamiltonian Floer theory
    Adv. Geom. (IF 0.736) Pub Date : 2020-04-28
    Oliver Fabert

    In this paper we show how the rich algebraic formalism of Eliashberg–Givental–Hofer’s symplectic field theory (SFT) can be used to define higher algebraic structures in Hamiltonian Floer theory. Using the SFT of Hamiltonian mapping tori we define a homotopy extension of the well-known Lie bracket and discuss how it can be used to prove the existence of multiple closed Reeb orbits. Furthermore we define

    更新日期:2020-04-28
  • Frontmatter
    Adv. Geom. (IF 0.736) Pub Date : 2020-04-28

    Journal Name: Advances in Geometry Volume: 20 Issue: 2 Pages: i-iii

    更新日期:2020-04-28
  • Some topics in differential geometry of normed spaces
    Adv. Geom. (IF 0.736) Pub Date : 2020-02-17
    Vitor Balestro; Horst Martini; Ralph Teixeira

    For a surface immersed in a three-dimensional space endowed with a smooth norm instead of an inner product, one can define analogous concepts of curvature and metric. With such concepts in mind, various questions immediately appear. The aim of this paper is to propose and answer some of those questions. In this framework we prove several characterizations of minimal surfaces in normed spaces, and respective

    更新日期:2020-02-17
  • Multiprojective witness sets and a trace test
    Adv. Geom. (IF 0.736) Pub Date : 2020-02-17
    Jonathan D. Hauenstein; Jose Israel Rodriguez

    In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness sets which encode the multidegree information of an irreducible multiprojective variety. Our main results generalise the regeneration solving procedure, a trace test, and numerical irreducible decomposition

    更新日期:2020-02-17
  • Extension of the Andersén–Lempert theory: Lie algebras of zero divergence vector fields on complex affine algebraic varieties
    Adv. Geom. (IF 0.736) Pub Date : 2020-02-17
    Fabrizio Donzelli

    For a smooth manifold X equipped with a volume form, let 𝓛0 (X) be the Lie algebra of volume preserving smooth vector fields on X. Lichnerowicz proved that the abelianization of 𝓛0 (X) is a finite-dimensional vector space, and that its dimension depends only on the topology of X. In this paper we provide analogous results for some classical examples of non-singular complex affine algebraic varieties

    更新日期:2020-02-17
  • Non-reduced moduli spaces of sheaves on multiple curves
    Adv. Geom. (IF 0.736) Pub Date : 2020-01-27
    Jean-Marc Drézet

    Some coherent sheaves on projective varieties have a non-reduced versal deformation space; for example, this is the case for most unstable rank 2 vector bundles on ℙ2, see []. In particular, some moduli spaces of stable sheaves are non-reduced. We consider some sheaves on ribbons (double structures on smooth projective curves): let E be a quasi locally free sheaf of rigid type and let 𝓔 be a flat

    更新日期:2020-01-27
  • Quaternionic equiangular lines
    Adv. Geom. (IF 0.736) Pub Date : 2020-01-27
    Boumediene Et-Taoui

    Let 𝔽 = ℝ, ℂ or ℍ. A p-set of equi-isoclinic n-planes with parameter λ in 𝔽r is a set of pn-planes spanning 𝔽r each pair of which has the same non-zero angle arccos λ. It is known that via a complex matrix representation, a pair of isoclinic n-planes in ℍr with angle arccos λ yields a pair of isoclinic 2n-planes in ℂ2r with angle arccos λ. In this article we characterize all the p-tuples of equi-isoclinic

    更新日期:2020-01-27
  • A note on norms of signed sums of vectors
    Adv. Geom. (IF 0.736) Pub Date : 2020-01-25
    Giorgos Chasapis; Nikos Skarmogiannis

    Improving a result of Hajela, we show for every function f with limn→∞f(n) = ∞ and f(n) = o(n) that there exists n0 = n0(f) such that for every n ⩾ n0 and any S ⊆ {–1, 1}n with cardinality |S| ⩽ 2n/f(n) one can find orthonormal vectors x1, …, xn ∈ ℝn satisfying ∥ε1x1+⋯+εnxn∥∞⩾clog⁡f(n) for all (ε1, …, εn) ∈ S. We obtain analogous results in the case where x1, …, xn are independent random points uniformly

    更新日期:2020-01-25
  • Topology of tropical moduli of weighted stable curves
    Adv. Geom. (IF 0.736) Pub Date : 2020-01-25
    Alois Cerbu; Steffen Marcus; Luke Peilen; Dhruv Ranganathan; Andrew Salmon

    The moduli space Δg,w of tropical w-weighted stable curves of volume 1 is naturally identified with the dual complex of the divisor of singular curves in Hassett’s spaces of w-weighted stable curves. If at least two of the weights are 1, we prove that Δ0, w is homotopic to a wedge sum of spheres, possibly of varying dimensions. Under additional natural hypotheses on the weight vector, we establish

    更新日期:2020-01-25
  • A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
    Adv. Geom. (IF 0.736) Pub Date : 2020-01-25
    Marilyn Breen

    Let 𝒞 be a finite family of distinct axis-parallel boxes in ℝd whose intersection graph is a tree, and let S = ⋃{C : C in 𝒞}. If every two points of S see a common point of S via k-staircase paths, then S is starshaped via k-staircase paths. Moreover, the k-staircase kernel of S will be convex via k-staircases.

    更新日期:2020-01-25
  • Three-dimensional connected groups of automorphisms of toroidal circle planes
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Brendan Creutz; Duy Ho; Günter F. Steinke

    We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.

    更新日期:2019-09-11
  • A maximum principle for circle-valued temperatures
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Andrew A. Cooper

    In this note we prove a ‘maximum principle’ for circle-valued solutions of the (time-dependent) heat equation on closed Riemannian manifolds.

    更新日期:2019-09-11
  • The integral polytope group
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Florian Funke

    We show that the Grothendieck group associated to integral polytopes in ℝn is free-abelian, by providing an explicit basis. Moreover, we identify the involution on this polytope group given by reflection about the origin as a sum of Euler characteristic type. We also compute the kernel of the norm map sending a polytope to its induced seminorm on the dual of ℝn.

    更新日期:2019-09-11
  • In simply connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Hiro Lee Tanaka

    Let Q be a simply connected manifold. We show that every exact Lagrangian cobordism between compact, exact Lagrangians in T*Q is an h-cobordism. This is a corollary of the Abouzaid–Kragh Theorem.

    更新日期:2019-09-11
  • Ricci almost solitons and contact geometry
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Amalendu Ghosh

    We prove that on a K-contact manifold, a Ricci almost soliton is a Ricci soliton if and only if the potential vector field V is a Jacobi field along the Reeb vector field ξ. Then we study contact metric as a Ricci almost soliton with parallel Ricci tensor. To this end, we consider Ricci almost solitons whose potential vector field is a contact vector field and prove some rigidity results.

    更新日期:2019-09-11
  • On pseudo-Einstein real hypersurfaces
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Mayuko Kon

    Let M be a real hypersurface of a complex space form Mn(c) with c ≠ 0 and n ≥ 3. We show that the Ricci tensor S of M satisfies S(X, Y) = ag(X, Y) for all vector fields X and Y on the holomorphic distribution, a being a constant, if and only if M is a pseudo-Einstein real hypersurface. By doing this we can give the definition of pseudo-Einstein real hypersurface under weaker conditions.

    更新日期:2019-09-11
  • Classification of slant surfaces in 𝕊3 × ℝ
    Adv. Geom. (IF 0.736) Pub Date : 2019-09-11
    Salvatore de Candia; Marian Ioan Munteanu

    We investigate slant surfaces in the almost Hermitian manifold 𝕊3 × ℝ, considering the position of the Reeb vector field ξ of the Sasakian structure on 𝕊3 with respect to the surfaces. We examine two cases: ξ normal or tangent to the surfaces. In the first case, we prove that every surface is totally real. In the second case, we characterize and locally describe complex surfaces. Finally, we completely

    更新日期:2019-09-11
  • An extension theorem for non-compact split embedded Riemannian symmetric spaces and an application to their universal property
    Adv. Geom. (IF 0.736) Pub Date : 2019-07-04
    Julius Grüning; Ralf Köhl

    By [] it is known that a geodesic γ in an abstract reflection space X (in the sense of Loos, without any assumption of differential structure) canonically admits an action of a 1-parameter subgroup of the group of transvections of X. In this article, we modify these arguments in order to prove an analog of this result stating that, if X contains an embedded hyperbolic plane 𝓗 ⊂ X, then this yields

    更新日期:2019-07-04
  • 𝔇⊥-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
    Adv. Geom. (IF 0.736) Pub Date : 2019-07-04
    Eunmi Pak; Young Jin Suh

    We study classifying problems for real hypersurfaces in a complex two-plane Grassmannian G2(ℂm+2). In relation to the generalized Tanaka–Webster connection, we consider a new concept of parallel normal Jacobi operator for real hypersurfaces in G2(ℂm+2) and prove that a real hypersurface in G2(ℂm+2) with generalized Tanaka–Webster 𝔇⊥-parallel normal Jacobi operator is locally congruent to an open part

    更新日期:2019-07-04
  • Exceptional points for finitely generated Fuchsian groups of the first kind
    Adv. Geom. (IF 0.736) Pub Date : 2019-06-30
    Joseph Fera; Andrew Lazowski

    Let G be a finitely generated Fuchsian group of the first kind and let (g : m1, m2, …, mn) be its shortened signature. Beardon showed that almost every Dirichlet region for G has 12g + 4n − 6 sides. Points in ℍ corresponding to Dirichlet regions for G with fewer sides are called exceptional for G. We generalize previously established methods to show that, for any such G, its set of exceptional points

    更新日期:2019-06-30
  • Continuous CM-regularity of semihomogeneous vector bundles
    Adv. Geom. (IF 0.736) Pub Date : 2019-06-30
    Alex Küronya; Yusuf Mustopa

    We ask when the CM (Castelnuovo–Mumford) regularity of a vector bundle on a projective variety X is numerical, and address the case when X is an abelian variety. We show that the continuous CM-regularity of a semihomogeneous vector bundle on an abelian variety X is a piecewise-constant function of Chern data, and we also use generic vanishing theory to obtain a sharp upper bound for the continuous

    更新日期:2019-06-30
  • Image Milnor number and 𝒜e-codimension for maps between weighted homogeneous irreducible curves
    Adv. Geom. (IF 0.736) Pub Date : 2019-06-22
    D. A. H. Ament; J. J. Nuño-Ballesteros; J. N. Tomazella

    Let (X, 0) ⊂ (ℂn, 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) → (ℂ2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that 𝒜e-codim(X, f) = μI(f), where the 𝒜e-codimension 𝒜e-codim(X, f) is the minimum number of parameters in a versal deformation and μI(f) is the image Milnor number, i.e. the number of vanishing

    更新日期:2019-06-22
  • On the order sequence of an embedding of the Ree curve
    Adv. Geom. (IF 0.736) Pub Date : 2019-06-22
    Dane C. Skabelund

    In this paper we compute the Weierstrass order-sequence associated with a certain linear series on the Deligne–Lusztig curve of Ree type. As a result, we show that the set of Weierstrass points of this linear series consists entirely of 𝔽q-rational points.

    更新日期:2019-06-22
  • Generalizations of 3-Sasakian manifolds and skew torsion
    Adv. Geom. (IF 0.736) Pub Date : 2019-04-12
    Ilka Agricola; Giulia Dileo

    In the first part, we define and investigate new classes of almost 3-contact metric manifolds, with two guiding ideas in mind: first, what geometric objects are best suited for capturing the key properties of almost 3-contact metric manifolds, and second, the new classes should admit ‘good’ metric connections with skew torsion. In particular, we introduce the Reeb commutator function and the Reeb Killing

    更新日期:2019-04-12
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