6 citations · 19 across the 15 of their papers we have counts for
15 papers
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…
Hermite--Einstein metrics in singular settings
Junyan Cao, Patrick Graf, Philipp Naumann +3
In this article we pursue the following main goals. In the first place, we establish the existence of "estimable" Hermite--Einstein metrics for stable reflexive coherent sheaves on…
On compact Kähler orbifold
Xiaojun Wu
In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact Kähler orbifold. In the second part, we shows various versi…
Albanese morphism of log smooth klt compact Kähler manifold with nef log anticanonical divisor
Xiaojun Wu
Let be an n-dimensional compact Kähler manifold. Let a divisor with simple normal crossings with such that $-(K_X…
Note on asymptotic behaviour of the canonical ring
Xiaojun Wu
The theory of the Oukounkov body is a useful tool for studying the asymptotic behaviour of the canonical ring of a line bundle over a projective manifold. In this note, combined wi…
Note on holomorphic Morse inequalities tensoring with a coherent sheaf
Xiaojun Wu
In this note, we show various versions of holomorphic Morse inequalities tensoring with a coherent sheaf.
On compact Kähler manifold with strongly pseudo-effective tangent bundle
Xiaojun Wu
In the first part of this note, we discuss the compact Kähler manifold with a strongly pseudo-effective tangent bundle. In the second part, we give new proof of the fact that the o…
The Bogomolov's inequality on a singular complex space
Xiaojun Wu
In this note, we prove the Bogomolov's inequality over a reduced, compact, irreducible, Kähler complex space that is smooth in codimension 2. The proof is obtained by a reduction t…
On a vanishing theorem due to Bogomolov
Xiaojun Wu
In this note, we give a new proof of a vanishing result originally due to Bogomolov, and later generalised by Mourougane and Boucksom. The statement holds for arbitrary pseudoeffec…
On Junyan Cao's vanishing theorem for pseudoeffective line bundles
Xiaojun Wu
Junyan Cao has obtained a very general vanishing theorem, valid on any compact Kähler manifold, for the cohomology groups with values in a pseudoeffective line bundle twisted by th…
On the Nakano vanishing theorem
Xiaojun Wu
In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.
Remark on nefness in higher codimension
Xiaojun Wu
In this work, following the fundamental work of Boucksom we construct the nef cone of a compact complex manifold in higher codimension and give explicit examples where these cones…
Intersection theory and Chern classes in Bott-Chern cohomology
Xiaojun Wu
In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of c…
Pseudo-effective and numerically flat reflexive sheaves
Xiaojun Wu
In this note, we discuss the concept of pseudoeffective vector bundle and also introduce pseudoeffective torsion-free sheaves over compact Kähler manifolds. We show that a pseudoef…
On the hard Lefschetz theorem for pseudoeffective line bundles
Xiaojun Wu
In this note, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result state…