A support theorem for the Hitchin fibration: the case of GLn and KC
| Autor: | Luca Migliorini, Jochen Heinloth, Mark Andrea A. de Cataldo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Fibration 0102 computer and information sciences 01 natural sciences Mathematics::Algebraic Topology Support theorem Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 010201 computation theory & mathematics Mathematics::K-Theory and Homology FOS: Mathematics 0101 mathematics Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Journal für die reine und angewandte Mathematik |
| Popis: | We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every $n \geq 3$. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over the versal deformations of spectral curves. Comment: 32 pages, exposition improved, rank 2 case clarified |
| Databáze: | OpenAIRE |
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