Maximality of moduli spaces of vector bundles on curves

Pub Date : 2021-11-22 DOI:10.46298/epiga.2023.8793
Erwan Brugall'e, Florent Schaffhauser
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引用次数: 3

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.
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曲线上向量束模空间的极大性
我们证明了非奇异实射影曲线上互质秩和阶的半稳定向量丛的模空间是极大实代数变种,当且仅当基曲线本身是极大的。这提供了一个新的极大变种家族,其成员具有任意大的维度。我们通过比较实轨迹的Betti数和复轨迹的Hodgunmbers来证明这一结果,并表明极大曲线上向量丛的模空间实际上满足一个比极大性更强的性质,我们称之为Hodge表示性。我们还简要介绍了已知这种性质的其他品种。
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