Shin-ichi Matsumura

activity

20102026

most citedA general extension theorem for cohomology classes on non reduced analytic spaces

39 citations · 187 across the 37 of their papers we have counts for

collaborators

38 papers

math.AG2026

Positivity of compact Kähler varieties admitting an int-amplified endomorphism

Shin-ichi Matsumura, Guolei Zhong

We study compact Kähler varieties admitting int-amplified endomorphisms from the viewpoint of positivity of tangent sheaves. Our main result shows that the tangent sheaf of such a…

math.AG2026

A note on compact Kähler varieties with pseudo-effective tangent sheaf

Shin-ichi Matsumura, Guolei Zhong

In this paper, we discuss recent developments and open problems concerning the geometry of compact Kähler varieties whose tangent sheaves are pseudo-effective in a strong sense. As…

math.AG2026

A flatness criterion for pseudo-effective sheaves on compact Kähler spaces

Junyan Cao, Ya Deng, Shin-ichi Matsumura

In this paper, we prove that if $E$ is a pseudo-effective sheaf with vanishing first Chern class on a klt compact Kähler space $X$ , then, after passing to a finite quasi-étale cove…

math.AG2025

Beauville--Bogomolov--Yau decomposition for Kähler generalized pairs

Shin-ichi Matsumura, Juanyong Wang, Xiaojun Wu +1

In this paper, we establish the Beauville--Bogomolov--Yau decomposition for generalized pairs in the Kähler setting, thereby extending this structure theorem to the natural framewo…

math.AG2025

On compact Kähler manifolds with pseudo-effective tangent bundle

Shin-ichi Matsumura, Chenghao Qing

In this paper, we prove that a compact Kähler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rational…

math.DG2025

Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature

Shin-ichi Matsumura

In this paper, we prove that a compact Kähler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $ϕ : X \to Y$ , where the fiber…

math.CV2024

Uniform $L^{2}$ -estimates for flat nontrivial line bundles on compact complex manifolds

Yoshinori Hashimoto, Takayuki Koike, Shin-ichi Matsumura

In this paper, we extend the uniform $L^{2}$ -estimate of $\partial ˉ$ -equations for flat nontrivial line bundles, proved for compact Kähler manifolds in the previous work, to com…

math.CV2024

Injectivity theorems for higher direct images under proper Kähler morphisms on snc spaces

Tsz On Mario Chan, Young-Jun Choi, Shin-ichi Matsumura

Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally Kähler…

math.AG2024

Singular Nakano positivity of direct image sheaves of adjoint bundles

Takahiro Inayama, Shin-ichi Matsumura, Yuta Watanabe

In this paper, we consider a proper Kähler fibration $f : X \to Y$ and a singular Hermitian line bundle $(L, h)$ on $X$ with semi-positive curvature. We prove that the direct…

math.AG2024

Minimal projective varieties satisfying Miyaoka's equality

Masataka Iwai, Shin-ichi Matsumura, Niklas Müller

In this paper, we establish a structure theorem for minimal projective klt varieties $X$ that satisfiy Miyaoka's equality $3 c_{2} (X) = c_{1} (X)^{2}$ . Specifically, we prove that the cano…

math.CV2024

Nakano positivity of singular Hermitian metrics: Approximations and applications

Takahiro Inayama, Shin-ichi Matsumura

This paper studies the approximation of singular Hermitian metrics on vector bundles using smooth Hermitian metrics with Nakano semi-positive curvature on Zariski open sets. We sho…

math.AG2023

Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations

Masataka Iwai, Shin-ichi Matsumura, Guolei Zhong

In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved o…

math.CV2023★ 1 cited

An injectivity theorem on snc compact Kähler spaces: an application of the theory of harmonic integrals on log-canonical centers via adjoint ideal sheaves

Tsz On Mario Chan, Young-Jun Choi, Shin-ichi Matsumura

Let $(X, D)$ be a log-canonical (lc) pair, in which $X$ is a compact Kähler manifold and $D$ is a reduced snc divisor, and let $F$ be a holomorphic line bundle on $X$ equipped with…

math.AG2023★ 3 cited

Compact Kähler three-folds with nef anti-canonical bundle

Shin-ichi Matsumura, Xiaojun Wu

In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishi…

math.AG2022

Open problems on structure of positively curved projective varieties

Shin-ichi Matsumura

We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smoo…

math.AG2022★ 4 cited

On the minimal model program for projective varieties with pseudo-effective tangent sheaf

Shin-ichi Matsumura

In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt…

math.AG2022★ 11 cited

The Nonvanishing problem for varieties with nef anticanonical bundle

Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell +2

We prove that if $(X, Δ)$ is a threefold pair with mild singularities such that $- (K_{X} + Δ)$ is nef, then the numerical class of $- (K_{X} + Δ)$ is effective.

math.AG2021★ 6 cited

Structure theorem for projective klt pairs with nef anti-canonical divisor

Shin-ichi Matsumura, Juanyong Wang

In this paper, we establish a structure theorem for projective klt pairs $(X, Δ)$ with nef anti-log canonical divisor; specifically, we prove that, up to replacing $X$ with a finite…

math.AG2021★ 5 cited

Strictly nef divisors on K-trivial fourfolds

Haidong Liu, Shin-ichi Matsumura

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on…

math.AG2020★ 5 cited

On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces

Sho Ejiri, Masataka Iwai, Shin-ichi Matsumura

In this paper, we study the relative anti-canonical divisor $- K_{X / Y}$ of an algebraic fiber space $ϕ : X \to Y$ , and we reveal relations among positivity conditions of $- K_{X / Y}$ ,…

math.AG2019★ 12 cited

Projective klt pairs with nef anti-canonical divisor

Frédéric Campana, Junyan Cao, Shin-ichi Matsumura

In this paper, we study a projective klt pair $(X, Δ)$ with the nef anti-log canonical divisor $- (K_{X} + Δ)$ and its maximally rationally connected fibration $ψ : X ⇢ Y$ .…

math.AG2019★ 21 cited

On projective manifolds with pseudo-effective tangent bundle

Genki Hosono, Masataka Iwai, Shin-ichi Matsumura

In this paper, we develop the theory of singular hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold $X$ with pseudo-effect…

math.AG2018★ 1 cited

Variation of numerical dimension of singular hermitian line bundles

Shin-ichi Matsumura

The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from…

math.DG2018★ 3 cited

On projective manifolds with semi-positive holomorphic sectional curvature

Shin-ichi Matsumura

In this paper, we establish a structure theorem for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. Our structure theorem contains the solution…

Positivity of compact Kähler varieties admitting an int-amplified endomorphism

A note on compact Kähler varieties with pseudo-effective tangent sheaf

A flatness criterion for pseudo-effective sheaves on compact Kähler spaces

Beauville--Bogomolov--Yau decomposition for Kähler generalized pairs

On compact Kähler manifolds with pseudo-effective tangent bundle

Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature

Uniform L2-estimates for flat nontrivial line bundles on compact complex manifolds

Injectivity theorems for higher direct images under proper Kähler morphisms on snc spaces

Singular Nakano positivity of direct image sheaves of adjoint bundles

Minimal projective varieties satisfying Miyaoka's equality

Nakano positivity of singular Hermitian metrics: Approximations and applications

Positivity of tangent sheaves of projective varieties -- the structure of MRC fibrations

An injectivity theorem on snc compact Kähler spaces: an application of the theory of harmonic integrals on log-canonical centers via adjoint ideal sheaves

Compact Kähler three-folds with nef anti-canonical bundle

Open problems on structure of positively curved projective varieties

On the minimal model program for projective varieties with pseudo-effective tangent sheaf

The Nonvanishing problem for varieties with nef anticanonical bundle

Structure theorem for projective klt pairs with nef anti-canonical divisor

Strictly nef divisors on K-trivial fourfolds

On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces

Projective klt pairs with nef anti-canonical divisor

On projective manifolds with pseudo-effective tangent bundle

Variation of numerical dimension of singular hermitian line bundles

On projective manifolds with semi-positive holomorphic sectional curvature

Uniform $L^{2}$ -estimates for flat nontrivial line bundles on compact complex manifolds