Teppei Takamatsu

Frobenius liftability of isolated complete intersections

Tatsuro Kawakami, Teppei Takamatsu

We classify Frobenius liftable normal isolated complete intersection singularities of dimension at least three over an algebraically closed field of positive characteristic. In dim…

math.AC2026

The WittVectors package for Macaulay2

Anne Fayolle, Abhay Goel, Devlin Mallory +2

We implement a Macaulay2 package for computations involving rings of truncated Witt vectors $W_{n} (R)$ of a finitely generated $\F_p$-algebra $R$ . This package includes ring operatio…

Some generalizations of Oort's conjecture

Ryosuke Shimada, Teppei Takamatsu

For a prime $p \geq 5$ , let $S_{g}$ be the moduli space over $F_{p}$ of $g$ -dimensional principally polarized supersingular abelian varieties. We show that e…

A cusp surface singularity is Frobenius liftable

Tatsuro Kawakami, Teppei Takamatsu

We show that a cusp surface singularity is Frobenius liftable. As a consequence, we determine all the Frobenius liftable surface singularities.

An explicit formula for the Artin invariant of smooth K3 hypersurfaces

Teppei Takamatsu, Shou Yoshikawa

We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi- $F$ -splitting. As an application, we obtain an explicit formula for this invariant.

Perfectoid pure thresholds of lifts of rational double points

Teppei Takamatsu, Shou Yoshikawa

We study the perfectoid pure threshold with respect to $p$ , an invariant of singularities in mixed characteristic $(0, p)$ arising from perfectoid purity. In this paper, we compute…

Non-quasi- $F$ -split canonical affine fourfolds exist in every characteristic

Teppei Takamatsu, Shou Yoshikawa

We construct canonical $Q$ -factorial Gorenstein affine fourfolds in every positive characteristic that are not quasi- $F$ -split.

Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic

Tetsushi Ito, Akihiro Kanemitsu, Teppei Takamatsu +1

We study prime Fano threefolds of genus 12 ( $V_{22}$ -varieties) with positive-dimensional automorphism groups in positive and mixed characteristic. We classify such varieties over…

math.AC2026

Quasi- $F^{\infty}$ -split height versus quasi- $F$ -regular height for rational double points and graded rings

Teppei Takamatsu, Shou Yoshikawa

In this paper, we study a phenomenon concerning quasi- $F$ -singularities: under suitable hypotheses, the finiteness of the quasi- $F^{\infty}$ -split height ( $ht^{\infty}$ ) i…

Quasi- $F$ -splitting and smooth weak del Pezzo surfaces in mixed characteristic

Hirotaka Onuki, Teppei Takamatsu, Shou Yoshikawa

We introduce the notion of quasi- $F$ -splitting in mixed characteristic and study Kodaira-type vanishing on quasi- $F$ -splitting varieties. As an application, we prove a Kodaira-type…

Fedder type criteria for quasi- $F$ -splitting II

Tatsuro Kawakami, Teppei Takamatsu, Shou Yoshikawa

In this paper, we apply Fedder-type criteria for quasi- $F$ -splitting to provide explicit computations of quasi- $F$ -split heights for Calabi-Yau hypersurfaces, bielliptic surfaces,…

Arithmetic monodromy of hyper-Kähler varieties over $p$ -adic fields

Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa +2

In this paper, we study the $p$ -adic and $ℓ$ -adic monodromy operators associated with hyper-Kähler varieties over $p$ -adic fields, in connection with Looijenga-Lunts-Verbitsky L…

Quintic del Pezzo threefolds in positive and mixed characteristic

Tetsushi Ito, Akihiro Kanemitsu, Teppei Takamatsu +1

We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism gr…

Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture

Lie Fu, Zhiyuan Li, Teppei Takamatsu +1

We investigate in this paper the so-called pointed Shafarevich problem for families of primitive symplectic varieties. More precisely, for any fixed pointed curve $(B, 0)$ and any…

Arithmetic finiteness of Mukai varieties of genus 7

Tetsushi Ito, Akihiro Kanemitsu, Teppei Takamatsu +1

We study arithmetic finiteness of prime Fano threefolds of genus 7 and their higher dimensional generalization, called Mukai varieties of genus 7. For prime Fano threefolds of genu…

Quasi-F-splittings in birational geometry III

Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka +3

We prove that $Q$ -Gorenstein quasi- $F$ -regular singularities are klt. To this end, we shall introduce quasi-test ideals.

On the supersingular locus of the Siegel modular variety of genus 3 or 4

Ryosuke Shimada, Teppei Takamatsu

We study the supersingular locus of the Siegel modular variety of genus 3 or 4. More concretely, we decompose the supersingular locus into a disjoint union of the product of a Deli…