Variations on cohomology rings and zero schemes
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908769250705408 |
|---|---|
| author | Rychlewicz, Kamil |
| author_facet | Rychlewicz, Kamil |
| contents | We extend the theorem of Hausel and the author from arXiv:2212.11836 that relates equivariant cohomology rings and algebras of functions on zero schemes. This paper combines three separate results. We prove that for a reductive group G acting on a smooth projective variety one can see the equivariant cohomology ring as the ring of functions on the zero scheme over the Kostant section, provided that some transversality condition is satisfied. In particular, we show that the conclusion holds for spherical varieties. We then show a version for singular varieties, e.g. discriminant varieties, where in general we only recover a part of equivariant cohomology ring, generated by Chern classes. We also show that an analogous result, connecting equivariant K-theory to the ring of functions on the fixed-point scheme, holds for GKM spaces.
This is a concise version of some results from the PhD thesis arXiv:2407.14659, which contains a broader introduction to the topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variations on cohomology rings and zero schemes Rychlewicz, Kamil Algebraic Geometry Algebraic Topology 14L30, 55N91 We extend the theorem of Hausel and the author from arXiv:2212.11836 that relates equivariant cohomology rings and algebras of functions on zero schemes. This paper combines three separate results. We prove that for a reductive group G acting on a smooth projective variety one can see the equivariant cohomology ring as the ring of functions on the zero scheme over the Kostant section, provided that some transversality condition is satisfied. In particular, we show that the conclusion holds for spherical varieties. We then show a version for singular varieties, e.g. discriminant varieties, where in general we only recover a part of equivariant cohomology ring, generated by Chern classes. We also show that an analogous result, connecting equivariant K-theory to the ring of functions on the fixed-point scheme, holds for GKM spaces. This is a concise version of some results from the PhD thesis arXiv:2407.14659, which contains a broader introduction to the topic. |
| title | Variations on cohomology rings and zero schemes |
| topic | Algebraic Geometry Algebraic Topology 14L30, 55N91 |
| url | https://arxiv.org/abs/2510.17493 |