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arXiv · 2212.01664

Counting rational curves with an $m$-fold point

Indranil Biswas·Chitrabhanu Chaudhuri·Apratim Choudhury·Ritwik Mukherjee·Anantadulal Paul
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Abstract

We obtain a recursive formula for the number of rational degree $d$ curves in $\mathbb{CP}^2$ that pass through $3d+1-m$ generic points and that have an $m$-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.

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Indranil Biswas, Chitrabhanu Chaudhuri, Apratim Choudhury, Ritwik Mukherjee, Anantadulal Paul. 2022-12-03. Counting rational curves with an $m$-fold point. https://doi.org/10.1016/j.aim.2023.109258

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