On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

• Autorzy: Zhiwei Wang
• Języki publikacji: EN

Abstrakty

EN

This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that $∂∂̅ω^{k} = 0$ for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle $K^{-1}_{X}$ is nef, then for any ε > 0, there is a smooth function $ϕ_{ε}$ on X such that $ω_{ε} := ω + i∂∂̅ϕ_{ε} > 0$ and Ricci $(ω_{ε}) ≥ -εω_{ε}$. Furthermore, if ω satisfies the assumption as above, we prove that for a Harder-Narasimhan filtration of $T_{X}$ with respect to ω, the slopes $μ_{ω}(ℱ_{i}/ℱ_{i-1})$ are nonnegative for all i; this generalizes a result of Cao which plays an important role in his study of the structures of Kähler manifolds.

Kategorie tematyczne

• 53C55: Hermitian and K\"ahlerian manifolds
• 32Q26: Notions of stability
• 31C10: Pluriharmonic and plurisubharmonic functions
• 32S45: Modifications; resolution of singularities
• 32J25: Transcendental methods of algebraic geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 117
• Numer: 1
• Strony: 41-58

Daty

wydano

2016

Twórcy

autor

Zhiwei Wang

• School of Mathematical Sciences, Peking University, Beijing 100871, China

Identyfikatory

DOI

10.4064/ap3780-11-2015