Gromov–Witten Invariants with Naive Tangency Conditions
Creators
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1.
University of Illinois Urbana-Champaign
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2.
California Institute of Technology
Abstract
We introduce Gromov–Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov–Witten invariants with naive tangency conditions in terms of descendent Gromov–Witten invariants. Several examples of genus zero Gromov–Witten invariants with naive tangencies are computed in the case of curves and surfaces. In particular, the counts of rational curves naively tangent to an anticanonical divisor on a del Pezzo surface are studied, and via mirror symmetry, we obtain a relation to the local Gromov–Witten invariants.
Copyright and License
© The Author(s) 2025. Published by Oxford University Press. All rights reserved.
Acknowledgement
We are grateful to M. Kontsevich who initially suggested a possible relationship between naive tangencies and descendent invariants. Discussions with Q. Chen, S. Guo, E. Ionel, D. Maulik, R. Pandharipande, and M. Porta were very helpful. Special thanks to A. Polishchuk and Y. Shen for organizing the workshop “Topics in Enumerative Geometry” at the University of Oregon in May 2022, during which we first exchanged ideas.
Communicated by Prof. Dragos Oprea
Funding
F.J. was partially supported by NSF grants DMS-2054830 and DMS-2239320. T.Y.Y. was partially supported by NSF grants DMS-2302095 and DMS-2245099.
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2310.13059 (arXiv)
Funding
- National Science Foundation
- DMS-2054830
- National Science Foundation
- DMS-2239320
- National Science Foundation
- DMS-2302095
- National Science Foundation
- DMS-2245099
Dates
- Accepted
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2025-09-11
- Available
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2025-10-14Published online