Marked and labelled Gushel-Mukai fourfolds

Brakkee, Emma; Pertusi, Laura

doi:10.1007/978-3-030-75421-1_6

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Marked and labelled Gushel-Mukai fourfolds

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Pertusi, Laura
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/978-3-030-75421-1_6
(Publisher version)

https://doi.org/10.48550/arXiv.2002.04248
(Preprint)

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Citation

Brakkee, E., & Pertusi, L. (2021). Marked and labelled Gushel-Mukai fourfolds. In G. Farkas (Ed.), Rationality of varieties (pp. 129-146). Cham: Birkhäuser.

Cite as: https://hdl.handle.net/21.11116/0000-0009-755B-E

Abstract

We prove that the moduli stacks of marked and labelled Hodge-special
Gushel-Mukai fourfolds are isomorphic. As an application, we construct rational
maps from the stack of Hodge-special Gushel-Mukai fourfolds of discriminant $d$
to the moduli space of (twisted) degree-$d$ polarized K3 surfaces. We use these
results to prove a counting formula for the number of 4-dimensional fibers of
Fourier-Mukai partners of very general Hodge-special Gushel-Mukai fourfolds
with associated K3 surface, and a lower bound for this number in the case of a
twisted associated K3 surface.