Rational cuspidal curves on del-Pezzo surfaces

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...

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Veröffentlicht in:arXiv.org 2015-09
Hauptverfasser: Biswas, Indranil, D'Mello, Shane, Mukherjee, Ritwik, Pingali, Vamsi
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2331-8422