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Moduli spaces of modules over even Clifford algebras and Prym varieties

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Abstract

A conic fibration has an associated sheaf of even Clifford algebras on the base. In this paper, we study the relation between the moduli spaces of modules over the sheaf of even Clifford algebras and the Prym variety associated to the conic fibration. In particular, we construct a rational map from the moduli space of modules over the sheaf of even Clifford algebras to the special subvarieties in the Prym variety, and check that the rational map is birational in some cases. As an application, we get an explicit correspondence between instanton bundles of minimal charge on cubic threefolds and twisted Higgs bundles on curves.

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Notes

  1. Note that we write a line bundle-valued quadratic form as \(q: L\rightarrow S^2F^\vee \) where the authors in [2] write it as \(L^\vee \rightarrow S^2F^\vee \).

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Acknowledgements

This paper is written as part of my Ph.D. thesis at the University of Pennsylvania. I would like to thank both my advisors Ron Donagi and Tony Pantev for their constant help, many discussions and encouragement. I would also like to thank Emanuele Macrì for many useful discussions and Alexander Kuznetsov for all the useful and detailed comments on the earlier drafts of this paper. I would also like to thank the reviewers for their careful reading and insightful comments.

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  1. Beijing International Center for Mathematical Research, Peking University, Jingchunyuan Courtyard #78, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China

    Jia Choon Lee

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Lee, J.C. Moduli spaces of modules over even Clifford algebras and Prym varieties. Math. Z. 304, 53 (2023). https://doi.org/10.1007/s00209-023-03310-w

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