Hodge-to-singular correspondence for reduced curves

Fuente: arXiv
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Main Authors: Mauri, Mirko, Migliorini, Luca
Format: Preprint
Published: 2022
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author Mauri, Mirko
Migliorini, Luca
author_facet Mauri, Mirko
Migliorini, Luca
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2205_11489
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Hodge-to-singular correspondence for reduced curves
Mauri, Mirko
Migliorini, Luca
Algebraic Geometry
14H60 (Primary) 14F06, 55N33 (Secondary)
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.
title Hodge-to-singular correspondence for reduced curves
topic Algebraic Geometry
14H60 (Primary) 14F06, 55N33 (Secondary)
url https://arxiv.org/abs/2205.11489