Effective computations of the AtiyahBott formula
Abstract
We present an implementation of the AtiyahBott residue formula for $\overline{M}_{0,m}(\mathbb{P}^{n},d)$. We use this implementation to compute a large number of GromovWitten 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.11183
 Bibcode:
 2021arXiv210511183M
 Keywords:

 Mathematics  Algebraic Geometry;
 14N10;
 14Q25;
 14N35;
 14C05;
 1404;
 53D12
 EPrint:
 Explanation of the algorithm, Computations with psiclasses and Jet bundles, Tables were updated to reflect the increased speed of computations due to the use of new Julia tools