Compact moduli spaces for slope-semistable sheaves

Abstract

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a projective n-fold and a curve C that arises as the complete intersection of n-1 very ample divisors, we construct a modular compactification of the moduli space of vector bundles that are slope-stable with respect to C. Our construction generalises the algebro-geometric construction of the Donaldson-Uhlenbeck compactification by Joseph Le Potier and Jun Li. Furthermore, we describe the geometry of the newly construced moduli spaces by relating them to moduli spaces of simple sheaves and to Gieseker-Maruyama moduli spaces.

v1: 41 pages, the threefold case, general case pending; v2: 51 pages, new features: generalisation of results to base manifolds of arbitrary dimension, identification of equivalence relation represented by the moduli space, comparison with Gieseker moduli spaces; v3: 50 pages, small corrections, updated references; a slightly shortened version will appear in "Algebraic Geometry"

References in corpus (1)

• Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation

Cited by in corpus (8)

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• A continuity theorem for families of sheaves on complex surfaces
• Complex algebraic compactifications of the moduli space of Hermitian-Yang-Mills connections on a projective manifold
• Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones
• Bounded sets of sheaves on relative analytic spaces
• Amplified endomorphisms of Fano fourfolds
• Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation
• Moduli spaces of slope-semistable sheaves with reflexive Seshadri graduations