论文标题
非架构量子k-invariants
Non-archimedean quantum K-invariants
论文作者
论文摘要
我们在非架构分析几何形状中构建量子k不变。与通过完美梗阻理论通过代数几何形状中的经典方法相反，我们基于以前的著作，基于衍生的非Archimedean几何形状的基础，可表示的定理和Gromov紧凑型。我们在衍生水平的稳定地图堆栈之间获得了自然几何关系的列表，就图形上的基本操作而言，即产品，产品，切割边缘，忘记尾巴和缩合边缘。他们立即暗示量子K不变的相应特性。派生的方法产生高度直观的陈述和功能证明。我们对量子k不变方法的派生方法的灵活性使我们不仅可以对标记点的简单发生条件施加，而且还可以施加多重性的发病率条件。这导致了一组新的枚举不变性。对于证据，我们在本文中进一步开发了衍生的非架构的几何形状的基础：我们研究了衍生的LCI形态，相对分析和对正常束的变形。我们的动机来自非章程列举的几何形状和镜像对称性。
We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our previous works on the foundations of derived non-archimedean geometry, the representability theorem and Gromov compactness. We obtain a list of natural geometric relations between the stacks of stable maps, directly at the derived level, with respect to elementary operations on graphs, namely, products, cutting edges, forgetting tails and contracting edges. They imply immediately the corresponding properties of quantum K-invariants. The derived approach produces highly intuitive statements and functorial proofs. The flexibility of our derived approach to quantum K-invariants allows us to impose not only simple incidence conditions for marked points, but also incidence conditions with multiplicities. This leads to a new set of enumerative invariants. For the proofs, we further develop the foundations of derived non-archimedean geometry in this paper: we study derived lci morphisms, relative analytification, and deformation to the normal bundle. Our motivations come from non-archimedean enumerative geometry and mirror symmetry.
