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Moduli Spaces of Cubic Threefolds and of Irreducible Holomorphic Symplectic Manifolds

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Birational Geometry and Moduli Spaces

Part of the book series: Springer INdAM Series ((SINDAMS,volume 39))

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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.

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Acknowledgements

The author wants to express her gratitude to S. Boissière and A. Sarti for reading a draft of this survey and to the Max Planck Institute of Mathematics for providing a great working environment. The comments of the anonymous referee, which the author gratefully appreciated, have greatly helped to improve and clarify the exposition.

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  1. Chiara Camere

    Present address: Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

Authors and Affiliations

  1. Max Planck Institute of Mathematics, Bonn, Germany

    Chiara Camere

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  1. Chiara Camere
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Correspondence to Chiara Camere .

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Editors and Affiliations

  1. Department of Mathematics, University of Milan, Milano, Italy

    Elisabetta Colombo

  2. SISSA - International School for Advanced Studies, Trieste, Italy

    Barbara Fantechi

  3. Department of Mathematics, University of Pavia, Pavia, Italy

    Paola Frediani

  4. Department of Mathematics, Università degli Studi di Bari, Bari, Italy

    Donatella Iacono

  5. Department of Mathematics, University of Pisa, Pisa, Italy

    Rita Pardini

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Camere, C. (2020). Moduli Spaces of Cubic Threefolds and of Irreducible Holomorphic Symplectic Manifolds. In: Colombo, E., Fantechi, B., Frediani, P., Iacono, D., Pardini, R. (eds) Birational Geometry and Moduli Spaces. Springer INdAM Series, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-030-37114-2_2

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