{"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/effective-computations-of-the-atiyah-bott","title":"Effective computations of the Atiyah-Bott formula","arxiv_id":"2105.11183","date":"2021-05-24","proceeding":null,"authors":["Giosuè Muratore","Csaba Schneider"],"abstract":"We present an implementation of the Atiyah-Bott residue formula for $\\overline{M}_{0,m}(\\mathbb{P}^{n},d)$. We use this implementation to compute a large number of Gromov-Witten invariants of genus $0$, including intersection numbers of rational curves on general complete intersections. We also compute some numbers of rational contact curves satisfying suitable Schubert conditions. Our computations confirm known predictions made by Mirror Symmetry. The code we developed for these problems is publicly available and can also be used for other types of computations.","url_abs":"https://arxiv.org/abs/2105.11183v3","url_pdf":"https://arxiv.org/pdf/2105.11183v3.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":"effective-computations-of-the-atiyah-bott","repo_url":"https://github.com/mgemath/AtiyahBott.jl","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}