Pseudo-effective and numerically flat reflexive sheaves
Algebraic Geometry
2022-04-29 v3 Complex Variables
Abstract
In this note, we discuss the concept of pseudoeffective vector bundle and also introduce pseudoeffective torsion-free sheaves over compact K\"ahler manifolds. We show that a pseudoeffective reflexive sheaf over a compact K\"ahler manifold with vanishing first Chern class is in fact a numerically flat vector bundle. A proof is obtained through a natural construction of positive currents representing the Segre classes of pseudoeffective vector bundles.
Cite
@article{arxiv.2004.14676,
title = {Pseudo-effective and numerically flat reflexive sheaves},
author = {Xiaojun Wu},
journal= {arXiv preprint arXiv:2004.14676},
year = {2022}
}
Comments
45 pages, final version