Enumerative geometry of hyperelliptic plane curves

Abstract

We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves of degree d and genus g passing through 3d+1 general points.

References in corpus (1)

• Counting curves of any genus on rational ruled surfaces

Cited by in corpus (8)

• Hodge integrals and degenerate contributions
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• The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution
• Counting curves of any genus on P^2_7
• A Fock Space approach to Severi Degrees of Hirzebruch Surfaces
• Positive divisors in symplectic geometry
• Descendant invariants and characteristic numbers