{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/modularity-of-landau-ginzburg-models","title":"Modularity of Landau-Ginzburg models","arxiv_id":"2307.15607","date":"2023-07-28","proceeding":null,"authors":["Charles Doran","Andrew Harder","Ludmil Katzarkov","Mikhail Ovcharenko","Victor Przyjalkowski"],"abstract":"For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open algebraic torus charts on which the potential function $w$ restricts to a Laurent polynomial satisfying a deformation of the Minkowski ansatz; the general fibres of $w$ are Dolgachev-Nikulin dual to the anticanonical hypersurfaces in $X$. To do this, we study the deformation theory of Landau-Ginzburg models in arbitrary dimension, following the third-named author, Kontsevich, and Pantev, specializing to the case of Landau-Ginzburg models obtained from Laurent polynomials. Our proof of Dolgachev-Nikulin mirror symmetry is by detailed case-by-case analysis, refining work of Cheltsov and the fifth-named author.","url_abs":"https://arxiv.org/abs/2307.15607v2","url_pdf":"https://arxiv.org/pdf/2307.15607v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"modularity-of-landau-ginzburg-models","repo_url":"https://github.com/MikhailOvcharenko/DN-duality","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}