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arXiv · 2004.14676

Pseudo-effective and numerically flat reflexive sheaves

Xiaojun Wu
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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.

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Xiaojun Wu. 2020-04-30. Pseudo-effective and numerically flat reflexive sheaves. https://arxiv.org/abs/2004.14676

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