论文标题
果皮和顶点代数的模量限制
Virasoro constraints on moduli of sheaves and vertex algebras
论文作者
论文摘要
在列举的几何形状中，Virasoro的约束首先是在Gromov-Witten理论中猜想的，在违反理论背景下有许多最新的发展。在本文中，我们根据来自乔伊斯（Joyce）的顶点代数中的自然保形矢量的主要状态来重现脱毛理论的Virasoro约束。这表明Virasoro的约束在墙壁交叉下保存。作为应用程序，我们通过将语句降低到等级1案例，证明了在任何曲线和仅具有$（P，P）$共同体类别的无扭转带轮的模量限制中的构成限制。
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf-theoretic Virasoro constraints in terms of primary states coming from a natural conformal vector in Joyce's vertex algebra. This shows that Virasoro constraints are preserved under wall-crossing. As an application, we prove the conjectural Virasoro constraints for moduli spaces of torsion-free sheaves on any curve and on surfaces with only $(p,p)$ cohomology classes by reducing the statements to the rank 1 case.
