Enumerative tropical algebraic geometry
Enumerative tropical algebraic geometry
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枚举热带代数几何
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
G. Mikhalkin
中科院分区：
文献类型：
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作者：
G. Mikhalkin
本文建立了环面中任意属曲线的枚举公式。结果表明，这样的曲线可以通过牛顿多边形中的某些点阵路径来计数。该公式于2010年早些时候公布。这个结果是借助所谓的热带代数几何建立起来的。这种几何结构允许用实空间Rn代替复环变分，用某些分段线性图代替全纯曲线。
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 [17]. The result is established with the help of the so-called tropical algebraic geometry. This geometry allows to replace complex toric varieties with the real space Rn and holomorphic curves with certain piecewise-linear graphs there.