English

Gromov--Witten invariants with naive tangency conditions

Algebraic Geometry 2023-10-23 v1 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.2310.13059,
  title  = {Gromov--Witten invariants with naive tangency conditions},
  author = {Felix Janda and Tony Yue Yu},
  journal= {arXiv preprint arXiv:2310.13059},
  year   = {2023}
}