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April 2021 On the existence of universal families of marked irreducible holomorphic symplectic manifolds
Eyal Markman
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Kyoto J. Math. 61(1): 207-223 (April 2021). DOI: 10.1215/21562261-2019-0075

Abstract

We prove the existence of a global family with natural universal properties over every component of the moduli space of marked irreducible holomorphic symplectic manifolds. The analogous result follows for Teichmüller spaces.

Acknowledgments

I thank Zhiyuan Li for his interesting talk, and for asking whether universal families exist over Teichmüller spaces of holomorphic symplectic manifolds, at the workshop “Hyper-Kähler Manifolds, Hodge Theory, and Chow Groups” at the Tsinghua Sanya International Mathematics Forum in December 2016. I thank the organizers, Radu Laza, Kieran O’Grady, and Claire Voisin for the invitation to this interesting and instructive workshop. I thank Daniel Huybrechts and Sukhendu Mehrotra for helpful communications and for their comments on an earlier draft of this article. I thank Jenia Tevelev for Remark 3.8. Finally, I thank the referees for numerous insightful comments and suggestions.

The author’s work was partially supported by Simons Foundation grant 427110.

Citation

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Eyal Markman. "On the existence of universal families of marked irreducible holomorphic symplectic manifolds." Kyoto J. Math. 61 (1) 207 - 223, April 2021. https://doi.org/10.1215/21562261-2019-0075

Information

Received: 16 March 2017; Revised: 19 March 2019; Accepted: 24 March 2019; Published: April 2021
First available in Project Euclid: 4 November 2020

Digital Object Identifier: 10.1215/21562261-2019-0075

Subjects:
Primary: 14J10
Secondary: 14D22

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 1 • April 2021
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