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 Mosc. Math. J., 2012, Volume 12, Number 4, Pages 863–879 (Mi mmj485)

A Note on Formality and Singularities of Moduli Spaces

Ziyu Zhang

Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

Abstract: This paper studies formality of the differential graded algebra $\mathrm{RHom}^\bullet(E,E)$, where $E$ is a semistable sheaf on a K3 surface. The main tool is Kaledin's theorem on formality in families. For a large class of sheaves $E$, this DG algebra is formal, therefore we have an explicit description of the singularity type of the moduli space of semistable sheaves at the point represented by $E$. This paper also explains why Kaledin's theorem fails to apply in the remaining case.

Key words and phrases: Formality, twistor family, moduli spaces of sheaves, hyperkähler.

DOI: https://doi.org/10.17323/1609-4514-2012-12-4-863-879

Full text: http://www.mathjournals.org/.../2012-012-004-011.html
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MSC: 14D20
Received: January 15, 2012; in revised form April 22, 2012
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Citation: Ziyu Zhang, “A Note on Formality and Singularities of Moduli Spaces”, Mosc. Math. J., 12:4 (2012), 863–879

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Arbarello E. Sacca G. Ferretti A., “Relative Prym Varieties Associated To the Double Cover of An Enriques Surface”, J. Differ. Geom., 100:2 (2015), 191–250
2. Arbarello E. Sacca G., “Singularities of Moduli Spaces of Sheaves on K3 Surfaces and Nakajima Quiver Varieties”, Adv. Math., 329 (2018), 649–703
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