39 citations · 187 across the 37 of their papers we have counts for
21 papers · 1 filter
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…
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…
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 is a pseudo-effective sheaf with vanishing first Chern class on a klt compact Kähler space , then, after passing to a finite quasi-étale cove…
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…
On compact Kähler manifolds with pseudo-effective tangent bundle
Shin-ichi Matsumura, Chenghao Qing
In this paper, we prove that a compact Kähler manifold with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rational…
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 and a singular Hermitian line bundle on with semi-positive curvature. We prove that the direct…
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 that satisfiy Miyaoka's equality . Specifically, we prove that the cano…
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…
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…
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…
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…
The Nonvanishing problem for varieties with nef anticanonical bundle
Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell +2
We prove that if is a threefold pair with mild singularities such that is nef, then the numerical class of is effective.
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 with nef anti-log canonical divisor; specifically, we prove that, up to replacing with a finite…
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…
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 of an algebraic fiber space , and we reveal relations among positivity conditions of ,…
Projective klt pairs with nef anti-canonical divisor
Frédéric Campana, Junyan Cao, Shin-ichi Matsumura
In this paper, we study a projective klt pair with the nef anti-log canonical divisor and its maximally rationally connected fibration .…
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 with pseudo-effect…
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…
A general extension theorem for cohomology classes on non reduced analytic spaces
Junyan Cao, Jean-Pierre Demailly, Shin-Ichi Matsumura
The main purpose of this paper is to generalize the celebrated L extension theorem of Ohsawa-Takegoshi in several directions : the holomorphic sections to extend are taken in…
Versions of injectivity and extension theorems
Yoshinori Gongyo, Shin-ichi Matsumura
We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combin…
Restricted volumes and divisorial Zariski decompositions
Shin-ichi Matsumura
We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, w…