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arXiv · 1812.09186

Gushel-Mukai varieties: moduli

Olivier Debarre·Alexander Kuznetsov
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Abstract

We describe the moduli stack of Gushel-Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comprehensive study of the relation between this stack and the stack of Lagrangian data; roughly speaking, we show that the former is a generalized root stack of the latter. As an application, we define the period map for Gushel-Mukai varieties and construct some complete nonisotrivial families of smooth Gushel-Mukai varieties. In an appendix, we describe a generalization of the root stack construction used in our approach to the moduli space.

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Olivier Debarre, Alexander Kuznetsov. 2018-12-21. Gushel-Mukai varieties: moduli. https://arxiv.org/abs/1812.09186

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