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

Abstract

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.

21 pages; to appear in Geometriae Dedicata. Comments are welcome

References in corpus (3)

• Enumerative geometry of elliptic curves on toric surfaces
• Rational cuspidal curves on del-Pezzo surfaces
• Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure