Pseudo-effective and numerically flat reflexive sheaves

Abstract

In this note, we discuss the concept of pseudoeffective vector bundle and also introduce pseudoeffective torsion-free sheaves over compact Kähler manifolds. We show that a pseudoeffective reflexive sheaf over a compact Kähler 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.

45 pages, final version

References in corpus (4)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Projective klt pairs with nef anti-canonical divisor
• Intersection theory and Chern classes in Bott-Chern cohomology
• Twisted cotangent bundles of Hyperkähler manifolds

Cited by in corpus (3)

• On projective manifolds with pseudo-effective tangent bundle
• Structure theorem for projective klt pairs with nef anti-canonical divisor
• On compact Kähler manifold with strongly pseudo-effective tangent bundle