Volumes of components of Lelong upper level sets II

2024/04/22 by Su, Shuang, Vu, Duc-Viet · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.14058

Abstract

Let X be a compact Kähler manifold of dimension n, and let T be a closed positive (1,1)-current in a nef cohomology class on X. We establish an optimal upper bound for the volume of components of Lelong upper level sets of T in terms of cohomology classes of non-pluripolar self-products of T.

Cited by

• Singularity of non-pluripolar cohomology classes
• Relative non-pluripolar product of currents on compact Hermitian manifolds

Related

• Volume of components of Lelong upper-level sets
• Loss of mass of non-pluripolar products
• Singularity of non-pluripolar cohomology classes
• Parabolic nef currents on hyperkaehler manifolds
• Monge-Ampère equations in big cohomology classes