Hodge-to-singular correspondence for reduced curves

Mirko Mauri; Luca Migliorini

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arXiv · 2205.11489

Hodge-to-singular correspondence for reduced curves

Mirko Mauri·Luca Migliorini

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Abstract

We study the summands of the decomposition theorem for the Hitchin system for $\mathrm{GL}_n$, in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.

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Mirko Mauri, Luca Migliorini. 2022-05-23. Hodge-to-singular correspondence for reduced curves. https://arxiv.org/abs/2205.11489

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