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Singularities of Bridgeland moduli spaces for K3 categories: an update (2307.07789v1)

Published 15 Jul 2023 in math.AG

Abstract: This survey is a continuation of the study undertaken in \cite{AS18}. We examine the local structure of Bridgeland moduli spaces $M_\sigma(v,\D)$, where the relevant triangulated category $\D$ is either the bounded derived category $\D=\Db(X)$ of a K3 surface $X$, or the Kuznetsov component $\D=\Ku(Y)\subset \D b(Y)$ of a smooth cubic fourfold $Y\subset \PP5$. For these moduli spaces, building on \cite{Bmm19}, \cite{Bmm21} 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 $\sigma$ 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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