论文标题
表面和虚拟不变的滑轮
Sheaves on surfaces and virtual invariants
论文作者
论文摘要
光滑的射杆表面上的稳定滑轮的模量大通常是单数。尽管如此，它们仍具有虚拟类别，该类别与希尔伯特（Hilbert of Point）的经典案例类似，可用于定义相交数字，例如虚拟欧拉（Virtual Euler）特征，Verlinde数字和Segre数字。我们调查了作者对这些数字的最新猜想，并将其应用于瓦法理论，$ k $ - 理论s-二元性，等级2 dijkgraaf-moore-moore-verlinde-verlinde-verlinde公式和虚拟的segre-segre-segre-verlinde通讯。 Mochizuki为后裔唐纳森不变的配方扮演的关键角色。
Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection numbers, such as virtual Euler characteristics, Verlinde numbers, and Segre numbers. We survey a set of recent conjectures by the authors for these numbers with applications to Vafa-Witten theory, $K$-theoretic S-duality, a rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula, and a virtual Segre-Verlinde correspondence. A key role is played by Mochizuki's formula for descendent Donaldson invariants.
