Hodge-to-singular correspondence for reduced curves
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929400756305920 |
|---|---|
| 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 |