Moduli spaces of cubic threefolds and of irreducible holomorphic symplectic 
manifolds

Camere, Chiara

doi:10.1007/978-3-030-37114-2_2

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Moduli spaces of cubic threefolds and of irreducible holomorphic symplectic manifolds

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Camere, Chiara
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/978-3-030-37114-2_2
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Camere, C. (2020). Moduli spaces of cubic threefolds and of irreducible holomorphic symplectic manifolds. In Birational geometry and moduli spaces (pp. 13-27). Cham: Springer.

Cite as: https://hdl.handle.net/21.11116/0000-0006-0D41-3

Abstract

In this survey, based on joint work of the author and S. Boissière and A. Sarti, we will describe an isomorphism between the moduli space of smooth cubic threefolds, as described by Allcock, Carlson and Toledo, and the moduli space of fourfolds of K3^[2]-type with a special non-symplectic automorphism of order three; then, I will show some consequences of this isomorphism concerning degenerations of non-symplectic automorphisms. Finally we will explore possible generalizations of the problem to higher dimensions and other moduli spaces of cubic threefolds.