{"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/geometry-of-the-mirror-models-dual-to-the","title":"Geometry of the mirror models dual to the complete intersection of two cubics","arxiv_id":"2311.15103","date":"2023-11-25","proceeding":null,"authors":["Mykola Pochekai"],"abstract":"We construct a natural crepant resolution of the Batyrev-Borisov mirror dual family to the complete intersection of two cubic hypersurfaces in $\\mathbb P^5$. It is, similarly to the mirrors of quintic threefolds, a family over $\\mathbb{P}^1$ with singular fibers over the set $\\{0, \\infty\\} \\cup \\mu_6$. We compute an explicit height function producing the MPCP desingularization of the $B$-model toric ambient space. We compute the limiting mixed Hodge structures of the singular fibers. We show that the singular fiber over $\\infty$ has maximal unipotent monodromy, whereas the singular fiber over $0$ is of a new type compared to the quintic case.","url_abs":"https://arxiv.org/abs/2311.15103v2","url_pdf":"https://arxiv.org/pdf/2311.15103v2.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":"geometry-of-the-mirror-models-dual-to-the","repo_url":"https://github.com/slowcodeproduction/mirror-ci2cubics-projectivity-check","is_official":1,"mentioned_in_paper":0,"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}