论文标题
量子K理论的国旗品种
Quantum K theory for flag varieties
论文作者
论文摘要
忘记来自部分标志的子空间会产生另一个由较少子空间组成的部分标志。这引起了相应标志品种之间的健忘地图$π：x \ to x'$。我们在这里证明，在一定程度上，与D稳定地图相关的多样性在Schubert品种中发送了明显的点$ x_i $ x $ x $是与其图像的合理连接的纤维，该纤维可以参数$π_* d $ stable地图，在Schubert varieties $ foug $ x_i $ x $ x $ x $ x'$ x $ x'$ x'$ x'$ x'$ x'$ x'$ x''中。这些品种的Euler特征是量子$ k $ invariants。我们的结果意味着量子$ K $相关器之间的平等性。我们将这些平等性扩展到模棱两可的环境。最后，我们研究了通用超平面$ fl_ {1，n-1} $的小量子$ k $ - 环。我们通过$ qk_s（fl_ {1，n-1}）$在$ qk_s中证明了一个奇瓦利公式，该公式通过对售出地图的空间到$ fl_ {1，n-1} $及其图像通过评估地图的几何分析。
Forgetting a subspace from a partial flag yields another partial flag composed of fewer subspaces. This induces a forgetful map $π: X \to X'$ between the corresponding flag varieties. We prove here that, for a degree large enough, the variety associated with degree d stable maps sending their marked points within Schubert varieties $X_i$ of $X$ is a rationally connected fibration over its image, which parametrizes degree $π_* d$ stable maps sending their marked points within the Schubert varieties $π(X_i)$ of $X'$. The Euler characteristic of these varieties are quantum $K$-invariants. Our result implies equalities between quantum $K$ correlators. We extend these equalities to the equivariant setting. Finally, we study the small quantum $K$-ring of the universal hyperplane $Fl_{1,n-1}$. We prove a Chevalley formula in $QK_s(Fl_{1,n-1})$ via geometrical analysis of the space of stale maps to $Fl_{1,n-1}$ and of its image via evaluation maps.
