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Marked and labelled Gushel-Mukai fourfolds

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arxiv 2002.04248 v1 pith:O4R2EKW7 submitted 2020-02-11 math.AG

Emma Brakkee , Laura Pertusi This is my paper
classification math.AG
keywords fourfoldsgushel-mukaihodge-specialassociatedlabelledmarkedmodulinumber
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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.

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