Effective computations of the Atiyah-Bott formula. (September 2022)

• Record Type: Journal Article
• Authors: Muratore, Giosuè; Schneider, Csaba
• Is Part Of: Journal of symbolic computation. Volume 112(2022)
• Page Start: 164
• Page End: 181
• Publication Date: 2022-09
• Subjects: 14N10 -- 14Q25 -- 14N35 -- 14C05 -- 14-04 -- 53D12; Contact -- Torus action -- Bott formula -- Enumeration -- SageMath -- Julia programming language; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.01.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present an implementation of the Atiyah-Bott residue formula for M ‾ 0, m ( 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.