In “J. Moduli of $p$-divisible groups” [9], Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours (“E. Cycles in the cohomology of Rapoport–Zink towers coming from the Lubin–Tate tower” [6]) to compute certain non-trivial $p$-adic étale cohomology classes appearing

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3, 6)$ for a family of K3 surfaces. We construct a good resolution of the Baily–Borel–Satake compactification of its parameter space, which admits special boundary points (LCSLs) given by normal crossing divisors. We find local isomorphisms between the $E(3, 6)$ systems and the associated GKZ systems defined locally on the

A CHL model is the quotient of $\mathrm{K}3 \times E$ by an order $N$ automorphism which acts symplectically on the $\mathrm{K}3$ surface and acts by shifting by an $N$-torsion point on the elliptic curve $E$. We conjecture that the primitive Donaldson–Thomas partition function of elliptic CHL models is a Siegel modular form, namely the Borcherds lift of the corresponding twisted-twined elliptic genera

We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell–Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations

A Weierstrass fibration is an elliptic fibration $Y \to B$ whose total space $Y$ may be given by a global Weierstrass equation in a $\mathbb{P}^2$‑bundle over $B$. In this note, we compute stringy Hirzebruch classes of singular Weierstrass fibrations associated with constructing non-Abelian gauge theories in $F$‑theory. For each Weierstrass fibration $Y \to B$ we then derive a generating function

This paper completes the classification problem which was proposed in the previous paper [1] in which we attempted to characterize the minimal models and families obtained by the tensor products and the simple current extensions of minimal models under the condition that the characters of simple modules satisfy modular differential equations of the third order, and a mild condition on vertex operator

We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension $n$ as a well formed complete intersection and it is not an intersection with a linear cone therein, then the weights of the weighted projective space do not exceed $n+1$. Based on this bound we classify all smooth Fano complete intersections of dimensions $4$ and $5$, and

We study the $E_1$-degeneration of the logarithmic Hodge to de Rham spectral sequence of the special fiber of a proper semistable family over a discrete valuation ring. On the one hand, we prove that the $E_1$-degeneration property is invariant under admissible blowups. Assuming functorial resolution of singularities over $\mathbb{Z}$, this implies that the $E_1$-degeneration property depends only

We show that the general Clifford double mirrors constructed in [BL18] (Lev Borisov and Zhan Li “On Clifford double mirrors of toric complete intersections”, Adv. Math., 328:300–355, 2018) are derived equivalent.

We analyze aspects of extant examples of 2d extremal chiral (super) conformal field theories with $c \leq 24$. These are theories whose only operators with dimension smaller or equal to $c/24$ are the vacuum and its (super) Virasoro descendants. The most prototypical example is the monster CFT, whose famous genus zero property is intimately tied to the Rademacher summability of its twined partition