论文标题
表面引号方案的虚拟K理论
The virtual K-theory of Quot schemes of surfaces
论文作者
论文摘要
我们在非弹射击表面上最多1个零件n的尺寸划线的数字标准的数字化的虚拟不变性。我们猜想，一系列虚拟K理论不变性的生成系列是由理性函数给出的。我们证明了几种几何形状的合理性，包括所有光滑的射影表面的守时商和p_g> 0的表面x的尺寸1。我们还表明，生成的一系列虚拟COBORDISM类可能是不合理的。 给定等级R的X理论类，我们将Virtual Segre和Verlinde数字的自然系列相关联。我们表明，Segre和Verlinde系列在以下三种情况下匹配：尺寸0的引用方案，点的希尔伯特方案和p_g> 0的表面上的曲线，引用了纤维类别支持的最小椭圆表面的方案。此外，对于排名n的微不足道的排交品的准确性，我们证明了segre/verlinde系列交换R和N的新对称性。Segre/verlinde语句具有与曲线相似的守时引号方案的类似物。
We study virtual invariants of Quot schemes parametrizing quotients of dimension at most 1 of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecture that the generating series of virtual K-theoretic invariants are given by rational functions. We prove rationality for several geometries including punctual quotients for all smooth projective surfaces and dimension 1 quotients for surfaces X with p_g>0. We also show that the generating series of virtual cobordism classes can be irrational. Given a K-theory class on X of rank r, we associate natural series of virtual Segre and Verlinde numbers. We show that the Segre and Verlinde series match in the following three cases: Quot schemes of dimension 0 quotients, Hilbert schemes of points and curves over surfaces with p_g>0, Quot schemes of minimal elliptic surfaces for quotients supported on fiber classes. Moreover, for punctual quotients of the trivial sheaf of rank N, we prove a new symmetry of the Segre/Verlinde series exchanging r and N. The Segre/Verlinde statements have analogues for punctual Quot schemes over curves.
