Multiplicity algebras for rank 2 bundles on curves of small genus

Nigel Hitchin

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arXiv · 2203.03424

Multiplicity algebras for rank 2 bundles on curves of small genus

Nigel Hitchin

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Abstract

Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra.

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BibTeX RIS

Nigel Hitchin. 2022-03-07. Multiplicity algebras for rank 2 bundles on curves of small genus. https://arxiv.org/abs/2203.03424

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