论文标题
次要粉丝，theta功能和卡拉比Yau对的模量
Secondary fan, theta functions and moduli of Calabi-Yau pairs
论文作者
论文摘要
我们猜想，三倍的模量$（x，e = e_1+\ dots+e_n，θ）的任何连接的组件$ q $其中，$ x $是一种平稳的投射变化，$ e $是一个正常的交叉交叉交叉的反典型分隔符，每$ e_i $ spame $ e_i $ umple is ample is ample is ample is ample is ample is ample is ample is ampe empe empe empe emple is ample emple emple emple，婚姻。更准确地说：请注意，$ Q $自然嵌入了稳定对的Kollár-Shepherd-Barron-Alexeev Moduli空间，我们猜测，诱导的紧凑型可以通过完整的孢子质品种允许有限的封面。我们构建了相关的完整曲线风扇，从而推广了Gelfand-Kapranov-Zelevinski次级风扇的反射性多面体。受镜像对称性的启发，我们推测了在这个复合品种上的普遍家族的合成结构，作为具有规范基础的分级代数捆绑的特点，其结构常数是由非Archimedean分析磁盘计数给出的。在Fano案件中，并假设镜子包含Zariski开放的圆环，我们构建了猜想的普遍家族，在曲折的情况下概括了Kapranov-Sturmfels-Zelevinski和Alexeev的家族。对于Del Pezzo表面，具有$（-1）$ - 曲线的反典型周期的曲线，我们证明了完整的猜想。
We conjecture that any connected component $Q$ of the moduli space of triples $(X,E=E_1+\dots+E_n,Θ)$ where $X$ is a smooth projective variety, $E$ is a normal crossing anti-canonical divisor with a 0-stratum, every $E_i$ is smooth, and $Θ$ is an ample divisor not containing any 0-stratum of $E$, is unirational. More precisely: note that $Q$ has a natural embedding into the Kollár-Shepherd-Barron-Alexeev moduli space of stable pairs, we conjecture that the induced compactification admits a finite cover by a complete toric variety. We construct the associated complete toric fan, generalizing the Gelfand-Kapranov-Zelevinski secondary fan for reflexive polytopes. Inspired by mirror symmetry, we speculate a synthetic construction of the universal family over this toric variety, as the Proj of a sheaf of graded algebras with a canonical basis, whose structure constants are given by counts of non-archimedean analytic disks. In the Fano case and under the assumption that the mirror contains a Zariski open torus, we construct the conjectural universal family, generalizing the families of Kapranov-Sturmfels-Zelevinski and Alexeev in the toric case. In the case of del Pezzo surfaces with an anti-canonical cycle of $(-1)$-curves, we prove the full conjecture.
