{"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-moduli-of-parabolic-bundles","title":"Geometry of the moduli of parabolic bundles on elliptic curves","arxiv_id":"1611.05417","date":"2016-11-16","proceeding":null,"authors":["Néstor Fernández Vargas"],"abstract":"The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\\mathbb{P}^1 \\times \\mathbb{P}^1$. We also showcase a special curve $\\Gamma$ isomorphic to $C$ embedded in this space, and this way we prove a Torelli theorem. This moduli space is related to the moduli space of semistable parabolic bundles over $\\mathbb{P}^1$ via a modular map which turns out to be the 2:1 cover ramified in $\\Gamma$. We recover the geometry of del Pezzo surfaces of degree 4 and we reconstruct all their automorphisms via elementary transformations of parabolic vector bundles.","url_abs":"http://arxiv.org/abs/1611.05417v1","url_pdf":"http://arxiv.org/pdf/1611.05417v1.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-moduli-of-parabolic-bundles","repo_url":"https://github.com/valentermz/Connections-on-elliptic-curves","is_official":0,"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}