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arXiv · 1409.6702

Enumeration of curves with two singular points

Somnath Basu·Ritwik Mukherjee
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Abstract

In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is at most 6. Our main tool is a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle V over M, counted with a sign, is the Euler class of V evaluated on the fundamental class of M.

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Somnath Basu, Ritwik Mukherjee. 2014-09-23. Enumeration of curves with two singular points. https://doi.org/10.1016/j.bulsci.2014.11.006

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