English

A Gromov-Witten theory for simple normal-crossing pairs without log geometry

Algebraic Geometry 2023-08-23 v2

Abstract

We define a new Gromov-Witten theory relative to simple normal crossing divisors as a limit of Gromov-Witten theory of multi-root stacks. Several structural properties are proved including relative quantum cohomology, Givental formalism, Virasoro constraints (genus zero) and a partial cohomological field theory. Furthermore, we use the degree zero part of the relative quantum cohomology to provide an alternative mirror construction of Gross-Siebert and to prove the Frobenius structure conjecture of Gross-Hacking-Keel.

Keywords

Cite

@article{arxiv.2008.04844,
  title  = {A Gromov-Witten theory for simple normal-crossing pairs without log geometry},
  author = {Hsian-Hua Tseng and Fenglong You},
  journal= {arXiv preprint arXiv:2008.04844},
  year   = {2023}
}

Comments

34 pages. Comments are welcome! v2: final version to appear in CMP

R2 v1 2026-06-23T17:47:04.082Z