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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213530 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862690036084899840 |
|---|---|
| author | Blomme, Thomas Carocci, Francesca |
| author_facet | Blomme, Thomas Carocci, Francesca |
| citation_txt | Correlated Gromov-Witten Invariants. Thomas Blomme and Francesca Carocci. SIGMA 21 (2025), 046, 49 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-17T20:39:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213530 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T20:39:16Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blomme, Thomas Carocci, Francesca 2026-02-18T11:26:10Z 2025 Correlated Gromov-Witten Invariants. Thomas Blomme and Francesca Carocci. SIGMA 21 (2025), 046, 49 pages 1815-0659 2020 Mathematics Subject Classification: 14N35; 14N10; 14J26 arXiv:2409.09472 https://nasplib.isofts.kiev.ua/handle/123456789/213530 https://doi.org/10.3842/SIGMA.2025.046 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. T.B. is supported by the SNF grant 204125; F.C. is supported by the Ambizione grant PZ00P2208699/1. F.C. is also partially supported by the MIUR Excellence Department Project MatMod@TOV, CUPE83C23000330006, awarded to the Department of Mathematics, University of Rome Tor Vergata, and also acknowledges the support of the PRIN Project “Moduli spaces and birational geometry” 2022L34E7W. The authors would like to thank D. Ranganathan, A. Kumaran, and S. Molcho for helpful discussions around the subject of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Correlated Gromov-Witten Invariants Article published earlier |
| spellingShingle | Correlated Gromov-Witten Invariants Blomme, Thomas Carocci, Francesca |
| title | Correlated Gromov-Witten Invariants |
| title_full | Correlated Gromov-Witten Invariants |
| title_fullStr | Correlated Gromov-Witten Invariants |
| title_full_unstemmed | Correlated Gromov-Witten Invariants |
| title_short | Correlated Gromov-Witten Invariants |
| title_sort | correlated gromov-witten invariants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213530 |
| work_keys_str_mv | AT blommethomas correlatedgromovwitteninvariants AT caroccifrancesca correlatedgromovwitteninvariants |