A Note on Singular Moduli Spaces of Sheaves on K3 Surfaces
Ziyu Zhang
TL;DR
This paper explores the relationships between singular moduli spaces of semistable sheaves on K3 surfaces, demonstrating how they can be connected through deformations and birational maps under specific conditions.
Contribution
It introduces new conditions under which different singular moduli spaces of sheaves on K3 surfaces are connected via deformations and birational transformations.
Findings
Moduli spaces of sheaves can be connected through deformations.
Birational maps relate different moduli spaces.
Conditions for connectivity depend on Mukai vectors.
Abstract
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension can be connected by deformations and birational maps.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models