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Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure

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arxiv 1511.04900 v2 pith:KSCPXVDN submitted 2015-11-16 math.AG math.SG

Indranil Biswas , Ritwik Mukherjee , Varun Thakre This is my paper · ORCID
classification math.AGmath.SG
keywords numbersurfacecomplexcurvesdel-pezzoenumerativefixedgenus
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We obtain a formula for the number of genus two curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This is done by extending the symplectic approach of Aleksey Zinger. This enumerative problem is expressed as the difference between the symplectic invariant and an intersection number on the moduli space of rational curves on the surface.

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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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