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Pseudo-effective and numerically flat reflexive sheaves

Research paper by Xiaojun Wu

Indexed on: 01 May '20Published on: 30 Apr '20Published in: arXiv - Mathematics - Algebraic Geometry



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.