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.
Cite
@article{arxiv.1303.2480,
title = {Compact moduli spaces for slope-semistable sheaves},
author = {Daniel Greb and Matei Toma},
journal= {arXiv preprint arXiv:1303.2480},
year = {2018}
}
Comments
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"