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arXiv · 1509.06300

Rational cuspidal curves on del-Pezzo surfaces

Indranil Biswas·Shane D'Mello·Ritwik Mukherjee·Vamsi Pingali
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Abstract

We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler class computation on the moduli space of curves. A topological method is employed in computing the contribution of the degenerate locus to this Euler class.

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Indranil Biswas, Shane D'Mello, Ritwik Mukherjee, Vamsi Pingali. 2015-09-21. Rational cuspidal curves on del-Pezzo surfaces. https://doi.org/10.5427/jsing.2018.17f

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