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arXiv · 2407.14832

On a fibre bundle version of the Caporaso-Harris formula

Indranil Biswas·Apratim Choudhury·Nilkantha Das·Ritwik Mukherjee
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Abstract

The Caporaso-Harris formula gives a recursive algorithm to enumerate delta nodal degree d curves in P^2. The recursion is obtained in terms of curves of lower degree that are tangent to a given divisor. This paper presents two generalizations of this method. The first result is on enumeration of one cuspidal curves on P^2, and the second result is an extension to the fiber bundle setting. We solve the question of counting the characteristic number planar nodal cubics in P^3 by extending the idea of Caporaso-Harris.

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Indranil Biswas, Apratim Choudhury, Nilkantha Das, Ritwik Mukherjee. 2024-07-20. On a fibre bundle version of the Caporaso-Harris formula. https://arxiv.org/abs/2407.14832

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