Atsushi Ito

activity

20122026

most citedDerived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

17 citations · 69 across the 26 of their papers we have counts for

collaborators

27 papers

math.AG2026

Remarks on basepoint-freeness thresholds of polarized abelian surfaces

Atsushi Ito

We determine the basepoint-freeness threshold of a very general polarized abelian surface over the field of complex numbers. We also give the first example of a polarized abelian s…

math.AG2026

Seshadri constants and Gromov widths of toric varieties associated with generalized permutohedra

Atsushi Ito

In this paper, we study the Seshadri constants and Gromov widths of polarized toric varieties whose moment polytopes are generalized permutohedra. We show that both invariants coin…

math.AG2026

Birational Geometry of Quot Schemes on smooth projective curves via Stable Pairs

Chandranandan Gangopadhyay, Atsushi Ito

Let $C$ be a smooth projective curve of genus $g \geq 2$ over $C$ , and let $E^{0}$ be a vector bundle on $C$ . We investigate the birational geometry of the Quot scheme ${\rm…

math.AG2025

Hyperbolicity of adjoint linear series on varieties with positive tangent bundle

Atsushi Ito, Joaquín Moraga, Debaditya Raychaudhury +1

Let $X$ be a smooth projective variety of dimension $n \geq 3$ , and let $L$ be an ample line bundle on $X$ . In this article, we study the algebraic hyperbolicity of a very general s…

math.AG2025

A remark on some punctual Quot schemes on smooth projective curves

Atsushi Ito

For a locally free sheaf $E$ on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of $E$ of length $n$ supp…

math.AG2025

On the Cox rings of some hypersurfaces

Andrew Pollock, Atsushi Ito, Balazs Szendroi

We introduce a cohomological method to compute Cox rings of hypersurfaces in the ambient space P^1 x P^n, which is more direct than existing methods. We prove that smooth hypersurf…

math.AG2022★ 2 cited

The movable cone of Calabi--Yau threefolds in ruled Fano manifolds

Atsushi Ito, Ching-Jui Lai, Sz-Sheng Wang

We describe explicitly the chamber structure of the movable cone for a general complete intersection Calabi--Yau threefold in a non-split $(n + 4)$ -dimensional $P^{n}$ -rul…

math.AG2022★ 1 cited

Projective normality and basepoint-freeness thresholds of general polarized abelian varieties

Atsushi Ito

For a polarized abelian variety $(X, L)$ , Z. Jiang and G. Pareschi introduce an invariant $β (X, L)$ , called the basepoint-freeness threshold. Using this invariant, we show that a gen…

math.AG2021★ 1 cited

M-regularity of $Q$ -twisted sheaves and its application to linear systems on abelian varieties

Atsushi Ito

G. Pareschi and M. Popa give criterions for global generations and surjectivity of multiplication maps of global sections of coherent sheaves on abelian varieties in the theory of…

math.AG2020★ 2 cited

Higher syzygies on general polarized abelian varieties of type $(1, \dots, 1, d)$

Atsushi Ito

In this paper, we show that a general polarized abelian variety $(X, L)$ of type $(1, \dots, 1, d)$ and dimension $g$ satisfies property $(N_{p})$ if $d \geq \sum_{i = 0}^{g} (p + 2)^{i}$ . In…

math.AG2019

Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups

Atsushi Ito

It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan construct a canonical filtration of the section ring, called Loewy filtrati…

math.AG2017★ 4 cited

Projective reconstruction in algebraic vision

Atsushi Ito, Makoto Miura, Kazushi Ueda

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In…

math.AG2017

On separable higher Gauss maps

Katsuhisa Furukawa, Atsushi Ito

We study the $m$ -th Gauss map in the sense of F.~L.~Zak of a projective variety $X \subset P^{N}$ over an algebraically closed field in any characteristic. For all integer $…

math.AG2016★ 17 cited

Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1

In this paper, we discuss the problem of whether the difference $[X] - [Y]$ of the classes of a Fourier--Mukai pair $(X, Y)$ of smooth projective varieties in the Grothendieck ring o…

math.AG2016★ 5 cited

$I$ -functions of Calabi--Yau 3-folds in Grassmannians

Daisuke Inoue, Atsushi Ito, Makoto Miura

We study $I$ -functions of Calabi--Yau 3-folds with Picard number one which are zero loci of general sections of direct sums of globally generated irreducible homogeneous vector bun…

math.AG2016★ 11 cited

Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians

Daisuke Inoue, Atsushi Ito, Makoto Miura

Based on the method by [Küc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles…

math.AG2016★ 15 cited

The class of the affine line is a zero divisor in the Grothendieck ring: via $G_{2}$ -Grassmannians

Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1

Motivated by [Bor] and [Mar], we show the equality $([X] - [Y]) \cdot [A^{1}] = 0$ in the Grothendieck ring of varieties, where $(X, Y)$ is a pair of Calabi-Yau 3…

math.AG2016

Calabi--Yau complete intersections in exceptional Grassmannians

Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1

We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we f…

math.AG2016★ 3 cited

A combinatorial description of dual defects of toric varieties

Katsuhisa Furukawa, Atsushi Ito

From a finite set in a lattice, we can define a toric variety embedded in a projective space. In this paper, we give a combinatorial description of the dual defect of the toric var…

math.AG2015

On Gauss maps in positive characteristic in view of images, fibers, and field extensions

Katsuhisa Furukawa, Atsushi Ito

The Gauss map of a projective variety $X \subset P^{N}$ is a rational map from $X$ to a Grassmann variety. In positive characteristic, we show the following results. (1) For…

math.AG2014

On birational geometry of the space of parametrized rational curves in Grassmannians

Atsushi Ito

In this paper, we study the birational geometry of the Quot schemes of trivial bundles on $P^{1}$ by constructing small $Q$ -factorial modifications of the Quot sche…

math.AG2014★ 1 cited

Gauss maps of toric varieties

Katsuhisa Furukawa, Atsushi Ito

We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1…

math.AG2013

Examples of Mori dream spaces with Picard number two

Atsushi Ito

In this note, we give a sufficient condition such that a projective variety with Picard number two is a Mori dream space. Using this condition, we obtain examples of Mori dream spa…

math.AG2013

Seshadri constants and degrees of defining polynomials

Atsushi Ito, Makoto Miura

In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as co…

Remarks on basepoint-freeness thresholds of polarized abelian surfaces

Seshadri constants and Gromov widths of toric varieties associated with generalized permutohedra

Birational Geometry of Quot Schemes on smooth projective curves via Stable Pairs

Hyperbolicity of adjoint linear series on varieties with positive tangent bundle

A remark on some punctual Quot schemes on smooth projective curves

On the Cox rings of some hypersurfaces

The movable cone of Calabi--Yau threefolds in ruled Fano manifolds

Projective normality and basepoint-freeness thresholds of general polarized abelian varieties

M-regularity of Q-twisted sheaves and its application to linear systems on abelian varieties

Higher syzygies on general polarized abelian varieties of type (1,…,1,d)

Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups

Projective reconstruction in algebraic vision

On separable higher Gauss maps

Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties

I-functions of Calabi--Yau 3-folds in Grassmannians

Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians

The class of the affine line is a zero divisor in the Grothendieck ring: via G2​-Grassmannians

Calabi--Yau complete intersections in exceptional Grassmannians

A combinatorial description of dual defects of toric varieties

On Gauss maps in positive characteristic in view of images, fibers, and field extensions

On birational geometry of the space of parametrized rational curves in Grassmannians

Gauss maps of toric varieties

Examples of Mori dream spaces with Picard number two

Seshadri constants and degrees of defining polynomials

M-regularity of $Q$ -twisted sheaves and its application to linear systems on abelian varieties

Higher syzygies on general polarized abelian varieties of type $(1, \dots, 1, d)$

$I$ -functions of Calabi--Yau 3-folds in Grassmannians

The class of the affine line is a zero divisor in the Grothendieck ring: via $G_{2}$ -Grassmannians