Erwan Brugallé ; Florent Schaffhauser - Maximality of moduli spaces of vector bundles on curves

epiga:8793 - Épijournal de Géométrie Algébrique, January 6, 2023, Volume 6 -
Maximality of moduli spaces of vector bundles on curves

Authors: Erwan Brugallé ; Florent Schaffhauser

    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.

    Volume: Volume 6
    Published on: January 6, 2023
    Accepted on: January 6, 2023
    Submitted on: December 2, 2021
    Keywords: Mathematics - Algebraic Geometry,14P25, 14H60

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