English

Theta functions, broken lines and 2-marked log Gromov-Witten invariants

Algebraic Geometry 2022-04-27 v1

Abstract

Theta functions were defined for varieties with effective anticanonical divisor and are related to certain punctured Gromov-Witten invariants. In this paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth very ample anticanonical divisor we can circumvent the notion of punctured Gromov-Witten invariants and relate theta functions and their multiplicative structure to certain 2-marked log Gromov-Witten invariants. This is a natural extension of the correspondence between wall functions and 1-marked log Gromov-Witten invariants.

Keywords

Cite

@article{arxiv.2204.12257,
  title  = {Theta functions, broken lines and 2-marked log Gromov-Witten invariants},
  author = {Tim Graefnitz},
  journal= {arXiv preprint arXiv:2204.12257},
  year   = {2022}
}

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27 pages