论文标题
微小量子K理论的阳性
Positivity of minuscule quantum K-theory
论文作者
论文摘要
我们证明，量子$ k $的舒伯特结构常数 - 任何微观标志品种或二次超出表面的戒指都具有与Codimension交替的符号。我们还证明，在量子共同体或量子$ k $ k $ k $的产品中发生的变形参数$ q $的功能 - cominuscule标志品种的响铃形成整数间隔。我们的证明是基于几个新结果，包括对任意标志歧管中两个舒伯特品种的最普遍的非空交集的明确描述，以及对限制在cominuscule标志品种中的任何负线束的同类套件的计算。我们还给出了量子到古典定理的类型均匀证明，该证明声称（3点，属0）Gromov-inginity不变的任何cominuscule标志品种的不变性是相关标志品种上的经典三重交流数。最后，我们证明了与该定理相关的几何和组合学的几个新结果。
We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$ that occur in the product of two Schubert classes in the quantum cohomology or quantum $K$-theory ring of a cominuscule flag variety form an integer interval. Our proofs are based on several new results, including an explicit description of the most general non-empty intersection of two Schubert varieties in an arbitrary flag manifold, and a computation of the cohomology groups of any negative line bundle restricted to a Richardson variety in a cominuscule flag variety. We also give a type-uniform proof of the quantum-to-classical theorem, which asserts that the (3-point, genus 0) Gromov-Witten invariants of any cominuscule flag variety are classical triple-intersection numbers on an associated flag variety. Finally, we prove several new results about the geometry and combinatorics related to this theorem.
