论文标题
热带正常功能 - 热带周期的较高的亚伯-Jacobi不变性
Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles
论文作者
论文摘要
我们考虑与热带品种家族相关的热带霍奇结构（TVH）的变化。相关的热带霍奇结构的热带中间雅各布人的家族定义了一堆热带雅各布人，我们称之为热带正常功能。我们将这些函数的形式顺序衍生物定义在基础上的天然高斯 - 曼宁连接方面，因为hodge理论不变性检测纤维中的热带周期。在热带类别中，归纳定义的相关不变剂是较高的Abel-Jacobi不变性。他们自然鉴定了热带食物组上的热带Bloch-Beilinson过滤。为了研究$ \ Mathcal {M} _ {g，n}^{\ text {trop}} $，我们在热带曲线的模量上检查了这种构造。期望是这些循环的非平凡性可以在热带类别中以较少的复杂性进行检查。该构建与方案类别的热带化函数兼容，上述过程还将提供一种替代方法来检查计划类别中$ \ Mathcal {M} _ {g，n} $的重言式环中的关系。
We consider the variation of tropical Hodge structure (TVHS) associated to families of tropical varieties. The family of the tropical intermediate Jacobians of the associated tropical Hodge structure defines a bundle of tropical Jacobians, whose sections we call the tropical normal functions. We define formal sequential derivatives of these functions on the base with respect to the natural Gauss-Manin connection as the Hodge theoretic invariants detecting tropical cycles in the fibers. The associated invariants which are defined inductively are the higher Abel-Jacobi invariants in the tropical category. They naturally identify the tropical Bloch-Beilinson filtration on the tropical Chow group. We examine this construction on the moduli of tropical curves with marked points, in order to study the tropical tautological classes in the tautological ring of $\mathcal{M}_{g,n}^{\text{trop}}$. The expectation is the nontriviality of these cycles could be examined with less complexity in the tropical category. The construction is compatible with the tropicalization functor on the category of schemes, and the aforementioned procedure will also provide an alternative way to examine the relations in the tautological ring of $\mathcal{M}_{g,n}$ in the schemes category.
