Thomas, Alexander (2021) Generalized punctual Hilbert schemes and $\mathfrak{g}$-complex structures. MPIM Preprint Series 2021 (12).
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Abstract
We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure from [FT19]. For real Lie algebras, this should give an alternative description of the Hitchin-Kostant-Rallis section defined in [GPR18].
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 3 Geometry and topology > 53-XX Differential geometry |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 23 Apr 2021 10:21 |
| Last Modified: | 18 May 2021 11:15 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4540 |
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