Counting rational curves with an $m$-fold point
Algebraic Geometry
2023-08-24 v2 Differential Geometry
Symplectic Geometry
Abstract
We obtain a recursive formula for the number of rational degree curves in that pass through generic points and that have an -fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.
Cite
@article{arxiv.2212.01664,
title = {Counting rational curves with an $m$-fold point},
author = {Indranil Biswas and Chitrabhanu Chaudhuri and Apratim Choudhury and Ritwik Mukherjee and Anantadulal Paul},
journal= {arXiv preprint arXiv:2212.01664},
year = {2023}
}
Comments
16 pages, 4 figures