Enumerative tropical algebraic geometry in R^2

Enumerative tropical algebraic geometry in R^2
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R^2 中的枚举热带代数几何

DOI：
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发表时间：
2003
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通讯作者：
G. Mikhalkin
G. Mikhalkin
中科院分区：
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文献类型：
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作者：
G. Mikhalkin

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本文建立了复曲面中任意亏格曲线的计数公式。事实证明，这些曲线可以通过牛顿多边形中的某些格路径来计数。该公式早些时候在这个http URL中公布 结果是建立在所谓的热带代数几何的帮助下。这种几何学允许人们用欧几里得n-空间和全纯曲线代替复环面的变种，用某些分段线性图代替。
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 this http URL 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.