论文标题
量子Lefschetz原理的分类
A categorification of the quantum Lefschetz principle
论文作者
论文摘要
量子Lefschetz公式解释了稳定地图的模量堆栈的虚拟基本类别（或结构束线）如何从环境目标方案传递到部分的零基因座时的表现。它仅在特殊假设（属$ 0 $，本节的规律性和捆绑包的凸）下有效。在本文中，我们使用派生的几何形状在几何级别上删除这些假设的一般性陈述。通过对衍生零基因座的结构或骨的研究，我们在$ \ infty $ - 级别$ cosherent滑轮分类中推断了该公式的分类。我们还证明，Manolache的虚拟回调可以构造为派生的回调，并在满足其假设时使用它们来恢复经典的量子Lefschetz公式。
The quantum Lefschetz formula explains how virtual fundamental classes (or structure sheaves) of moduli stacks of stable maps behave when passing from an ambient target scheme to the zero locus of a section. It is only valid under special assumptions (genus $0$, regularity of the section and convexity of the bundle). In this paper, we give a general statement at the geometric level removing these assumptions, using derived geometry. Through a study of the structure sheaves of derived zero loci we deduce a categorification of the formula in the $\infty$-categories of quasi-coherent sheaves. We also prove that Manolache's virtual pullbacks can be constructed as derived pullbacks, and use them to recover the classical Quantum Lefschetz formula when its hypotheses are satisfied.
