Quantum Steenrod operations of symplectic resolutions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912744065728512 |
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| author | Lee, Jae Hee |
| author_facet | Lee, Jae Hee |
| contents | We study the mod $p$ equivariant quantum cohomology of conical symplectic resolutions. Using symplectic genus zero enumerative geometry, Fukaya and Wilkins defined operations on mod $p$ quantum cohomology deforming the classical Steenrod operations on mod $p$ cohomology. We conjecture that these quantum Steenrod operations on divisor classes agree with the $p$-curvature of the mod $p$ equivariant quantum connection, and verify this in the case of the Springer resolution. The key ingredient is a new compatibility relation between the quantum Steenrod operations and the shift operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02100 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Steenrod operations of symplectic resolutions Lee, Jae Hee Symplectic Geometry Algebraic Geometry Representation Theory 53D45 We study the mod $p$ equivariant quantum cohomology of conical symplectic resolutions. Using symplectic genus zero enumerative geometry, Fukaya and Wilkins defined operations on mod $p$ quantum cohomology deforming the classical Steenrod operations on mod $p$ cohomology. We conjecture that these quantum Steenrod operations on divisor classes agree with the $p$-curvature of the mod $p$ equivariant quantum connection, and verify this in the case of the Springer resolution. The key ingredient is a new compatibility relation between the quantum Steenrod operations and the shift operators. |
| title | Quantum Steenrod operations of symplectic resolutions |
| topic | Symplectic Geometry Algebraic Geometry Representation Theory 53D45 |
| url | https://arxiv.org/abs/2312.02100 |