Correlated Gromov-Witten Invariants
We introduce a geometric refinement of Gromov-Witten invariants for ℙ¹-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore, we prove a refinement of the degeneration formula, keeping track of the correlation....
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213530 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Correlated Gromov-Witten Invariants. Thomas Blomme and Francesca Carocci. SIGMA 21 (2025), 046, 49 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We introduce a geometric refinement of Gromov-Witten invariants for ℙ¹-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore, we prove a refinement of the degeneration formula, keeping track of the correlation. Finally, combining certain invariance properties of the correlated invariant, a local computation, and the refined degeneration formula, we follow floor diagram techniques to prove regularity results for the generating series of the invariants in the case of ℙ¹-bundles over elliptic curves. Such invariants are expected to play a role in the degeneration formula for reduced Gromov-Witten invariants for abelian and K3 surfaces.
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| ISSN: | 1815-0659 |