Effective computations of the Atiyah-Bott formula

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.

Explanation of the algorithm, Computations with psi-classes and Jet bundles, Tables were updated to reflect the increased speed of computations due to the use of new Julia tools

Cited by in corpus (2)

• Enumeration of rational contact curves via torus actions
• Irreducible Contact Curves via Graph Stratification