Moduli of Reflexive Sheaves on Smooth Projective 3-folds

2005/04/22 by Peter Vermeire, Vermeire, Peter
Mathematics · #14D20 #14F05 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14D20 #msc:14F05 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0504465

17 pages. Entire paper rewritten - discusses relationship between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves; brief mention of Donaldson-Thomas invariants

openalex publication_date 2005/04/22 · arxiv created 2006/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves.

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