Movable curves and semistable sheaves

Abstract

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on singular varieties, as well as a characterisation of finite quotients of Abelian varieties via a Chern class condition.

24 pages, 2 figures; v2: various minor corrections as requested by referees, will appear in International Mathematics Research Notices

References in corpus (2)

• Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties
• Compact moduli spaces for slope-semistable sheaves

Cited by in corpus (8)

• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• Geometry and stability of tautological bundles on Hilbert schemes of points
• Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor
• Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
• On global ACC for foliated threefolds
• Stable vector bundles on generalized Kummer varieties
• On the Semistability of certain Lazarsfeld-Mukai bundles on Abelian surfaces
• Stability and certain ${\mathbb{P}}^n$-functors