arXiv subjects

Yongpan Zou

Publications and source records attributed to Yongpan Zou.

9 recordsLinked to original sources

arXiv2026

Variation of Kahler-Einstein metrics with mixed singularities

In this short note, we consider a fiberation f: (X, Delta) to Y between two compact Kahler manifolds with generic fiber of f being a smooth log canonical pair with ample canonical divisor, we prove that the current induced by variation of Kahler Einsteins with mixed cone and Poincare singularities is positive, hence generalize the result of Schumacher in the smooth case [22] and the result of Guenancia in the conic case [14]. As application, we prove the surjectivity of Albanese map for a smooth log canonical pair with -(KX + Delta) being nef.

math.DG↗

arXiv2025

Logarithmic Akizuki--Nakano vanishing theorems on weakly pseudoconvex Kähler manifolds

In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex Kähler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on compact Kähler manifolds. We derive vanishing theorems for certain direct image sheaves as a direct corollary.

math.CV↗

arXiv2025

On the Kodaira dimension of some algebraic fiber spaces

In this paper, we study the descent of positivity of the canonical bundle along fiber spaces. As a consequence, we prove a conjecture of Schnell, establishing the equivalence between the Non-vanishing Conjecture and its generalized version proposed by Campana and Peternell.

math.AG↗

arXiv2024

Nakano Positivity of direct image sheaves of adjoint line bundles with mild singularities

In this note, we generalized Berndtsson's result about the Nakano positivity of direct image sheaves to some special singular cases.

math.AG↗

arXiv2024

On the direct image of the adjoint big and nef line bundles

We investigate the positivity properties of the direct image $f_{\ast}(K_{X/Y} \otimes L)$ of the adjoint line bundle associated with a big and nef line bundle $L$, under a smooth fibration $f: X\to Y$ between projective varieties. We show that the vector bundle $f_{\ast}(K_{X/Y} \otimes L)$ is big.

math.AG↗

arXiv2023

On the Kodaira--Saito vanishing theorem of weakly ample divisor

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

math.AG↗

arXiv2022

Note on the singular Hermitian metrics with analytic singularities

We study the sheaf of locally square integrable holomorphic section of vector bundle with semi-positive curved singular Hermitian metric. We confirm the coherence when its induced determinant metric has analytic singularities.

math.CV↗

arXiv2019

On the Morse--Novikov Cohomology of blowing up complex manifolds

Inspired by the recent works of S. Rao--S. Yang--X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse--Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse--Novikov cohomology by introducing the relative Morse--Novikov cohomology group via sheaf cohomology theory and presenting the explicit isomorphism therein.

math.DG↗

arXiv2019

On Tian-Todorov lemma and its applications to deformation of CR-structures

We give a new Tian-Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of $d'd''$-lemma, more faithfully following Tian-Todorov's approach.

math.CV↗