Maximality of moduli spaces of vector bundles on curves

Brugallé, Erwan; Schaffhauser, Florent

doi:10.46298/epiga.2023.8793

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Maximality of moduli spaces of vector bundles on curves

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Schaffhauser, Florent
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.46298/epiga.2023.8793
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https://doi.org/10.48550/arXiv.2111.10959
(Preprint)

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Brugalle-Schaffhauser_Maximality of moduli spaces pf vector bundes on curves_2022.pdf
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Citation

Brugallé, E., & Schaffhauser, F. (2022). Maximality of moduli spaces of vector bundles on curves. Épijournal de Géométrie Algébrique, 6: 24. doi:10.46298/epiga.2023.8793.

Cite as: https://hdl.handle.net/21.11116/0000-000C-4792-F

Abstract

We prove that moduli spaces of semistable vector bundles of coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if the base curve itself is maximal. This provides a new family of maximal varieties, with members of arbitrarily large dimension. We prove the result by comparing the Betti numbers of the real locus to the Hodge numbers of the complex locus and showing that moduli spaces of vector bundles over a maximal curve actually satisfy a property which is stronger than maximality and that we call Hodge-expressivity. We also give a brief account on other varieties for which this property was already known.