On the descendent Gromov-Witten theory of a K3 surface
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908700530180096 |
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| author | Oberdieck, Georg |
| author_facet | Oberdieck, Georg |
| contents | We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that allows to remove descendent insertions of $1$ in many instances. Together this yields an efficient way to compute a large class of invariants (modulo the conjecture on the stationary part). As a corollary we conjecture a surprising polynomial structure which underlies the Gromov-Witten invariants of the K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09074 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the descendent Gromov-Witten theory of a K3 surface Oberdieck, Georg Algebraic Geometry We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that allows to remove descendent insertions of $1$ in many instances. Together this yields an efficient way to compute a large class of invariants (modulo the conjecture on the stationary part). As a corollary we conjecture a surprising polynomial structure which underlies the Gromov-Witten invariants of the K3 surface. |
| title | On the descendent Gromov-Witten theory of a K3 surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2308.09074 |