Compact moduli spaces for slope-semistable sheaves
50 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5599ae20bb7f31683b7c866276a9741fed696452
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In Geometry and Topology
- Stefan Kebekus
- T. Peternell
- D. Greb
- S. Druel
- Henri Guenancia
- Carolina Araujo
- A. Höring
- Benjamin Bakker
In Mathematical Physics
Citations in the corpus
- Movable curves and semistable sheaves (2014, methodology): “In a different direction, the paper [11] uses polarizations by movable curves to resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional varieties.”