Enumerative tropical algebraic geometry in R2
代数几何
2007-05-23 v4 数学物理
组合数学
几何拓扑
math.MP
辛几何
摘要
The paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in the Newton polygon. The formula was announced earlier in http://arxiv.org/abs/math.AG/0209253. The result is established with the help of the so-called tropical algebraic geometry. This geometry allows one to replace complex toric varieties with the Euclidean n-space and holomorphic curves with certain piecewise-linear graphs there.
引用
@article{arxiv.math/0312530,
title = {Enumerative tropical algebraic geometry in R2},
author = {Grigory Mikhalkin},
journal= {arXiv preprint arXiv:math/0312530},
year = {2007}
}
备注
83 pages, 20 figures, Version 4, to appear in the Journal of the AMS