论文标题
希尔伯特（Hilbert）的后裔系列的合理性和表面的引用方案
Rationality of descendent series for Hilbert and Quot schemes of surfaces
论文作者
论文摘要
每当商Sheaf具有最多的一维支持时，X带有完美的阻塞理论和虚拟基本类别的引号X带有完美的阻塞理论和虚拟基本类别的引号。当简单地连接X时，相关的生成一系列虚拟Euler特性被认为是一个有理函数。我们在这里猜想了更一般的后裔系列的合理性，并从重言式捆的Chern特征获得的插入量。我们证明了所有曲线类别的希尔伯特方案案例中后裔系列的合理性以及曲线类别为0时的引号案例。
Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series of virtual Euler characteristics was conjectured to be a rational function when X is simply connected. We conjecture here the rationality of more general descendent series with insertions obtained from the Chern characters of the tautological sheaf. We prove the rationality of descendent series in Hilbert scheme cases for all curve classes and in Quot scheme cases when the curve class is 0.
