论文标题
Abelian表面中的热带曲线II：线性系统中曲线的枚举
Tropical curves in abelian surfaces II: enumeration of curves in linear systems
论文作者
论文摘要
在本文中，第二部分中的三个部分，我们给出了一个对应定理，以将阿贝尔表面的固定线性系统中的$ g $曲线计数与热带计数相关联。为此，我们将由复杂曲线定义的线性系统与曲线中循环上1形的某些积分定义的线性系统联系起来。然后，我们给出了对应定理提供的热带多样性的表达式，并证明了相关的精制多样性的不变性，从而在Abelian表面引入了Block-Göttsche类型的精制不变性。
In this paper, second installment in a series of three, we give a correspondence theorem to relate the count of genus $g$ curves in a fixed linear system in an abelian surface to a tropical count. To do this, we relate the linear system defined by a complex curve to certain integrals of 1-forms over cycles in the curve. We then give an expression for the tropical multiplicity provided by the correspondence theorem, and prove the invariance for the associated refined multiplicity, thus introducing refined invariants of Block-Göttsche type in abelian surfaces.
