Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure
Algebraic Geometry
2025-02-21 v2 Symplectic Geometry
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.
Cite
@article{arxiv.1511.04900,
title = {Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure},
author = {Indranil Biswas and Ritwik Mukherjee and Varun Thakre},
journal= {arXiv preprint arXiv:1511.04900},
year = {2025}
}
Comments
21 pages; to appear in Geometriae Dedicata. Comments are welcome