The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry
Algebraic Geometry
2007-08-01 v3
Abstract
Some years ago Caporaso and Harris have found a nice way to compute the numbers N(d,g) of complex plane curves of degree d and genus g through 3d+g-1 general points with the help of relative Gromov-Witten invariants. Recently, Mikhalkin has found a way to reinterpret the numbers N(d,g) in terms of tropical geometry and to compute them by counting certain lattice paths in integral polytopes. We relate these two results by defining an analogue of the relative Gromov-Witten invariants and rederiving the Caporaso-Harris formula in terms of both tropical geometry and lattice paths.
Keywords
Cite
@article{arxiv.math/0504392,
title = {The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry},
author = {Andreas Gathmann and Hannah Markwig},
journal= {arXiv preprint arXiv:math/0504392},
year = {2007}
}
Comments
23 pages; update to match the published version