Towards refined curve counting on the Enriques surface I: K-theoretic refinements
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913453864648704 |
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| author | Oberdieck, Georg |
| author_facet | Oberdieck, Georg |
| contents | We conjecture an explicit formula for the $K$-theoretically refined Vafa-Witten invariants of the Enriques surface. By a wall-crossing argument the conjecture is equivalent to a new conjectural formula for the K-theoretically refined Pandharipande-Thomas invariants of the local Enriques surface. Evidence for the conjecture is given in several cases. We also comment on the case of K3 surfaces previously studied by Thomas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards refined curve counting on the Enriques surface I: K-theoretic refinements Oberdieck, Georg Algebraic Geometry We conjecture an explicit formula for the $K$-theoretically refined Vafa-Witten invariants of the Enriques surface. By a wall-crossing argument the conjecture is equivalent to a new conjectural formula for the K-theoretically refined Pandharipande-Thomas invariants of the local Enriques surface. Evidence for the conjecture is given in several cases. We also comment on the case of K3 surfaces previously studied by Thomas. |
| title | Towards refined curve counting on the Enriques surface I: K-theoretic refinements |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.21318 |