Equivariant Hodge modules and rational singularities
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909148343435264 |
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| author | Arapura, Donu Hiatt, Scott |
| author_facet | Arapura, Donu Hiatt, Scott |
| contents | We define a notion of Hodge modules with rational singularities. A variety has rational singularities in the usual sense, if it is normal and the Hodge module related to intersection cohomology has rational singularities in the present sense. Our main result is a generalization of Boutot's theorem that if a reductive group acts on an affine variety with a stable point, and $H$ is an equivariant Hodge module with rational singularities, then the induced module on the GIT quotient also has rational singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01947 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equivariant Hodge modules and rational singularities Arapura, Donu Hiatt, Scott Algebraic Geometry 14B05, 14F10, 14L39 We define a notion of Hodge modules with rational singularities. A variety has rational singularities in the usual sense, if it is normal and the Hodge module related to intersection cohomology has rational singularities in the present sense. Our main result is a generalization of Boutot's theorem that if a reductive group acts on an affine variety with a stable point, and $H$ is an equivariant Hodge module with rational singularities, then the induced module on the GIT quotient also has rational singularities. |
| title | Equivariant Hodge modules and rational singularities |
| topic | Algebraic Geometry 14B05, 14F10, 14L39 |
| url | https://arxiv.org/abs/2212.01947 |