Skip to main content

Research Repository

Advanced Search

The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map

You, Fenglong

The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map Thumbnail


Authors



Abstract

Given a smooth log Calabi–Yau pair (X,D), we use the intrinsic mirror symmetry construction to define the mirror proper Landau–Ginzburg potential and show that it is a generating function of two-point relative Gromov–Witten invariants of (X,D). We compute certain relative invariants with several negative contact orders, and then apply the relative mirror theorem of Fan et al. (Sel Math (NS) 25(4): Art. 54, 25, 2019. https://doi.org/10.1007/s00029-019-0501-z) to compute two-point relative invariants. When D is nef, we compute the proper Landau–Ginzburg potential and show that it is the inverse of the relative mirror map. Specializing to the case of a toric variety X, this implies the conjecture of m Gräfnitz et al. (2022) that the proper Landau–Ginzburg potential is the open mirror map. When X is a Fano variety, the proper potential is related to the anti-derivative of the regularized quantum period.

Citation

You, F. (2024). The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map. Communications in Mathematical Physics, 405(3), Article 79. https://doi.org/10.1007/s00220-024-04954-3

Journal Article Type Article
Acceptance Date Jan 30, 2024
Online Publication Date Mar 12, 2024
Publication Date 2024-03
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 405
Issue 3
Article Number 79
DOI https://doi.org/10.1007/s00220-024-04954-3
Public URL https://nottingham-repository.worktribe.com/output/46726564
Publisher URL https://link.springer.com/article/10.1007/s00220-024-04954-3
Additional Information Received: 17 November 2023; Accepted: 30 January 2024; First Online: 12 March 2024; : ; : The author has no competing interests to declare that are relevant to the content of this article.

Files

The Proper Landau–Ginzburg Potential, Intrinsic Mirror Symmetry and the Relative Mirror Map (617 Kb)
PDF

Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





You might also like



Downloadable Citations