Pluripotential theory on compact Hermitian manifolds

In this paper we establish the following Kawamata-Viehweg type vanishing theorem on a compact K¨ahler manifold or, more generally, a normal compact K¨ ahler space..

Projective variety, K¨ ahler manifold, Hodge theory, positive current, Monge- Amp`ere equation, Lelong number, Chern connection, curvature, Bochner-Kodaira tech- nique,

This survey presents various results concerning the geometry of compact K¨ ahler manifolds with numerically effective first Chern class: structure of the Albanese morphism of

The proof relies on a clever iteration procedure based on the Ohsawa-Takegoshi L 2 extension theorem, and a convergence process of an analytic nature (no algebraic proof at present

The idea is to show the existence of a 4-dimensional complex torus X = C 4 /Λ which does not contain any analytic subset of positive dimension, and such that the Hodge classes of

The latter conjecture asserts that every entire curve drawn on a projective variety of general type should satisfy a global algebraic equation; via a probabilistic

Non-zero holomorphic p-forms on a compact K¨ahler manifold X with − K X nef vanish only on the singular locus of the refined HN filtration of T ∗ X... Smoothness of the

Non-zero holomorphic p-forms on a compact K¨ ahler manifold X with − K X nef vanish only on the singular locus of the refined HN filtration of T ∗ X. This implies the following