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Rational cuspidal curves on del-Pezzo surfaces

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arxiv 1509.06300 v1 pith:4KJJQYES submitted 2015-09-21 math.AG math.SG

Indranil Biswas , Shane D'Mello , Ritwik Mukherjee , Vamsi Pingali This is my paper · ORCID
classification math.AGmath.SG
keywords curvesclasscuspidaldel-pezzoeulernumberrationalsurface
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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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  1. Counting curves in a linear system with upto eight singular points

    math.AG 2019-09 conditional novelty 7.0 of 10

    The authors derive recursive Euler class formulas that enumerate curves with δ nodes and one fixed singularity for all δ+k ≤ 8, recovering prior results and producing new codimension eight numbers.

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