Correspondence theorems via tropicalizations of moduli spaces
Correspondence theorems via tropicalizations of moduli spaces
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通过模空间热带化的对应定理
DOI：
10.1142/s0219199715500431
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发表时间：
2014
影响因子：
1.6
通讯作者：
Andreas Gross
中科院分区：
文献类型：
--
作者：
Andreas Gross
我们证明了环面簇中不可约标记参数化标记有理曲线的模空间可以嵌入代数环面中，使得它们的热带化是类似的热带模空间。这些嵌入被证明尊重评估态射，因为评估与热带化相互交换。考虑到这种特殊的情况，我们证明了枚举问题的一般对应定理，这些问题是通过代数和热带世界中的“评估图”定义的。将其应用到我们的动机示例中，我们表明给定环面品种中曲线的热带化，其与内部的边界约数相交并具有规定的重数，并通过适当数量的通用点，正是满足类似条件的相应热带环面品种中的热带曲线。此外，理论上定义的热带曲线的交集重数等于对其进行热带化的代数曲线的数量。
We show that the moduli spaces of irreducible labeled parametrized marked rational curves in toric varieties can be embedded into algebraic tori such that their tropicalizations are the analogous tropical moduli spaces. These embeddings are shown to respect the evaluation morphisms in the sense that evaluation commutes with tropicalization. With this particular setting in mind, we prove a general correspondence theorem for enumerative problems which are defined via “evaluation maps” in both the algebraic and tropical world. Applying this to our motivational example, we show that the tropicalizations of the curves in a given toric variety which intersect the boundary divisors in their interior and with prescribed multiplicities, and pass through an appropriate number of generic points are precisely the tropical curves in the corresponding tropical toric variety satisfying the analogous condition. Moreover, the intersection-theoretically defined multiplicities of the tropical curves are equal to the numbers of algebraic curves tropicalizing to them.
热带拟阵品种和周期交叉点的对角线
影响因子：
1.1
作者：
G. François;J. Rau
通讯作者：
J. Rau