论文标题
飞机对称产品的不良皮带
Perverse sheaves on symmetric products of the plane
论文作者
论文摘要
对于任何字段$ k $，我们对类别$ \ mathrm {perv} _ \ mathscr {s}（s^n（\ mathbb {c}^2），k）的$ n $ flperse sheaves的$ n $ - flpers $ s^n（\ s^n（c）\ s^n（c）\ s^n（c \ c} 2） $ k $的系数。特别是，我们表明它等于与Schur代数密切相关的新代数上的模块类别。作为我们描述的一部分，我们获得了希尔伯特方案的模块化弹簧理论的类似物，$ \ mathrm {hilb}^n（\ mathbb {c}^2）$ n $点的$ n $点$ n $ point在飞机上，其希尔伯特·chow-chow-chow-chow morphism。
For any field $k$, we give an algebraic description of the category $\mathrm{Perv}_\mathscr{S}(S^n (\mathbb{C}^2),k)$ of perverse sheaves on the $n$-fold symmetric product of the plane $S^n(\mathbb{C}^2)$ constructible with respect to its natural stratification and with coefficients in $k$. In particular, we show that it is equivalent to the category of modules over a new algebra that is closely related to the Schur algebra. As part of our description we obtain an analogue of modular Springer theory for the Hilbert scheme $\mathrm{Hilb}^n(\mathbb{C}^2)$ of $n$ points in the plane with its Hilbert-Chow morphism.
