论文标题
多根堆栈和应用的镜像定理
A mirror theorem for multi-root stacks and applications
论文作者
论文摘要
给定一个平滑的投射品种$ x $，带有简单的正常交叉除数$ d：= d_1+d_2+...+d_n $，其中$ d_i \ subset x $是光滑的，不可约的和nef的。我们通过构造$ i $ function，这是gromov for gromov的$ i $ function，证明了多根堆叠$ x_ {d，\ vec r} $的镜像定理。我们提供三个应用程序：（1）我们表明，对于足够大的$ \ vec r $，$ x_ {d，\ vec r}的某些零属不变性稳定。 （2）我们陈述了一个广义的本地遗传学原理猜想，并证明了它的版本。 （3）我们表明，使用$ x_ {d，\ vec r} $的Orbifold不变式的Fano品种的正则量子量与镜像Landau的经典时期相吻合。
Given a smooth projective variety $X$ with a simple normal crossing divisor $D:=D_1+D_2+...+D_n$, where $D_i\subset X$ are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks $X_{D,\vec r}$ by constructing an $I$-function, a slice of Givental's Lagrangian cone for Gromov--Witten theory of multi-root stacks. We provide three applications: (1) We show that some genus zero invariants of $X_{D,\vec r}$ stabilize for sufficiently large $\vec r$. (2) We state a generalized local-log-orbifold principle conjecture and prove a version of it. (3) We show that regularized quantum periods of Fano varieties coincide with classical periods of the mirror Landau--Ginzburg potentials using orbifold invariants of $X_{D,\vec r}$.
