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Erschienen in:
2021 | OriginalPaper | Buchkapitel
Marked and Labelled Gushel–Mukai Fourfolds
verfasst von : Emma Brakkee, Laura Pertusi
Erschienen in: Rationality of Varieties
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We prove that the moduli stacks of marked and labelled Hodgespecial 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 fourdimensional 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.