论文标题
通过超级黎曼表面的模量空间的枚举几何形状
Enumerative geometry via the moduli space of super Riemann surfaces
论文作者
论文摘要
在本文中，我们将超级Riemann表面的模量空间与稳定的Riemann表面的模量空间$ \ OVERLINE {\ CAL M} _ {G，N} $相关联。这使我们能够通过代数几何形状证明，在斯坦福大学和维滕通过超级几何技术证明了超级双曲线表面的模量空间之间的递归。事实证明，超级双曲表面的模量空间之间的递归相当于以下事实：在$ \ overline {\ cal m} _ {\ cal m} _ {g，n} $ a的自然共同集合$θ_{g，n} $的自然集合$θ_{g，n} $的生成函数中这类似于Mirzakhani在$ \ Overline {\ cal M} _ {g，n} $上使用多体性表面的模量空间的kontsevich-witten定理证明了kontsevich-witten-witten定理的重言式函数的生成函数。
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the volumes of moduli spaces of super hyperbolic surfaces previously proven via super geometry techniques by Stanford and Witten. The recursion between the volumes of moduli spaces of super hyperbolic surfaces is proven to be equivalent to the fact that a generating function for the intersection numbers of a natural collection of cohomology classes $Θ_{g,n}$ with tautological classes on $\overline{\cal M}_{g,n}$ is a KdV tau function. This is analogous to Mirzakhani's proof of the Kontsevich-Witten theorem regarding a generating function for the intersection numbers of tautological classes on $\overline{\cal M}_{g,n}$ using volumes of moduli spaces of hyperbolic surfaces.
