{"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/examples-violating-golyshev-s-canonical-strip","title":"Examples violating Golyshev's canonical strip hypotheses","arxiv_id":"1806.07648","date":"2018-06-20","proceeding":null,"authors":["Pieter Belmans","Sergey Galkin","Swarnava Mukhopadhyay"],"abstract":"We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomials of polarised varieties. They are given by moduli spaces of rank 2 bundles with fixed odd-degree determinant on curves of sufficiently high genus, hence our Fano examples have Picard rank 1, index 2, are rational, and have moduli. The hypotheses also fail for several other closely related varieties.","url_abs":"https://arxiv.org/abs/1806.07648v1","url_pdf":"https://arxiv.org/pdf/1806.07648v1.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":"examples-violating-golyshev-s-canonical-strip","repo_url":"https://github.com/pbelmans/canonical-strip-moduli-of-vector-bundles","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"examples-violating-golyshev-s-canonical-strip","repo_url":"https://github.com/pbelmans/ehrhart-polynomials-toric-fanos","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}