Singularities of Bridgeland moduli spaces for K3 categories: an update

2023/07/15 by Enrico Arbarello, Arbarello, Enrico, Giulia Saccà +1 · 3 citations
Mathematics · #!6G20 #14B05 #14D20 #14J28 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.07789

openalex publication_date 2023/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey is a continuation of the study undertaken in \citeAS18. We examine the local structure of Bridgeland moduli spaces M_σ(v,\D), where the relevant triangulated category \D is either the bounded derived category \D=\D^b(X) of a K3 surface X, or the Kuznetsov component \D=\Ku(Y)⊂ \D ^b(Y) of a smooth cubic fourfold Y⊂ \PP⁵. For these moduli spaces, building on \citeBmm19, \citeBmm21 we give a direct proof of formality and, using their local isomorphism with quiver varieties, we establish their normality and their irreducibility, as long as σ does not lie on a totally semistable wall. We then connect the variation of GIT quotients for quiver varieties with the changing of stability conditions on moduli spaces.

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• Some examples of moduli spaces on surfaces via wall-crossing
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