# Gushel–Mukai varieties: Moduli

@article{Debarre2020GushelMukaiVM,
title={Gushel–Mukai varieties: Moduli},
author={Olivier Debarre and Alexander Kuznetsov},
journal={International Journal of Mathematics},
year={2020}
}
• Published 21 December 2018
• Mathematics
• International Journal of Mathematics
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 so-called Lagrangian data defined in our previous works; 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…

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