A Gromov–Witten Theory for Simple Normal-Crossing Pairs Without Log Geometry

Tseng, Hsian-Hua; You, Fenglong

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 and Siebert (Intrinsic mirror symmetry, arXiv:1909.07649) and to prove the Frobenius structure conjecture of Gross et al. (Publ Math Inst Hautes Études Sci 122:65–168, 2015) in our setting.

Citation

Tseng, H.-H., & You, F. (2023). A Gromov–Witten Theory for Simple Normal-Crossing Pairs Without Log Geometry. Communications in Mathematical Physics, 401(1), 803-839. https://doi.org/10.1007/s00220-023-04656-2

• Journal Article Type: Article
• Acceptance Date: Jan 18, 2023
• Online Publication Date: Feb 11, 2023
• Publication Date: 2023-07
• Deposit Date: Mar 16, 2025
• Publicly Available Date: Mar 17, 2025
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 401
• Issue: 1
• Pages: 803-839
• DOI: https://doi.org/10.1007/s00220-023-04656-2
• Public URL: https://nottingham-repository.worktribe.com/output/46726579
• Publisher URL: https://link.springer.com/article/10.1007/s00220-023-04656-2
• Additional Information: Received: 12 April 2022; Accepted: 18 January 2023; First Online: 11 February 2023