Moduli of non-pure sheaves and contractions of Hilbert schemes

2025/08/18 by Herrero, Andres Fernandez, Makarova, Svetlana
#14D23 (Primary) 14D20 #14E05 #14F08 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.13395

Abstract

We define certain stacks of rank one sheaves on a smooth projective variety, and show that they admit proper good moduli spaces. We offer several applications to contractions of subschemes inside Hilbert schemes of points. We construct a surgery diagram via non-GIT wall-crossing, and use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata's DK-hypothesis in this setting.

Citations

• S-equivalence for algebraic stacks
• A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks
• Moduli spaces of sheaves via affine Grassmannians
• Uhlenbeck compactification as a Bridgeland moduli space
• The étale local structure of algebraic stacks
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• Birational geometry and derived categories
• On the structure of instability in moduli theory
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• The Minimal Model Program for the Hilbert Scheme of Points on P² and Bridgeland Stability
• Good moduli spaces for Artin stacks
• Tame stacks in positive characteristic
• Stability conditions on triangulated categories
• Deformation theory of singular symplectic n-folds
• Flops and derived categories
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Fourier-Mukai transforms for K3 and elliptic fibrations

Related

• K-theory of moduli spaces of sheaves and large Grassmannians
• Moduli spaces of sheaves via affine Grassmannians
• Sklyanin algebras and Hilbert schemes of points
• The geometry of the moduli space of one-dimensional sheaves
• Wall crossing for derived categories of moduli spaces of sheaves on\n rational surfaces