论文标题
实现阿贝尔表面的热带曲线
Realization of tropical curves in abelian surfaces
论文作者
论文摘要
我们在实际Tori中的热带曲线开始，在Abelian表面中构建代数曲线。我们为在真正的圆环中的热带曲线提供了必要和充分的条件，可以通过ABELIAN表面的代数曲线实现。当满足条件时，可以通过组合公式计算代数曲线的数量。这为我们提供了类似于Mikhalkin的曲面表面的代数 - 热带对应定理。换句话说，可以通过热带曲线纯粹地计算出穿过阿贝尔表面中通用点的代数曲线数量。
We construct algebraic curves in abelian surfaces starting from tropical curves in real tori. We give a necessary and sufficient condition for a tropical curve in a real torus to be realizable by an algebraic curve in an abelian surface. When the condition is satisfied, the number of algebraic curves can be computed by a combinatorial formula. This gives us an algebraic-tropical correspondence theorem for abelian surfaces analogous to Mikhalkin's correspondence theorem for toric surfaces. In other words, the number of algebraic curves passing through generic points in an abelian surface can be computed purely combinatorially via tropical curves.
