关于超Riemann Surfaces的劈裂变形问题
On The Problem of Splitting Deformations of Super Riemann Surfaces
摘要：
超黎曼曲面$\mathcal S$的奇变形是由奇宇称变量对$\mathcal S$的变形。本文研究了$\mathcal S$的奇形变$\mathcal X$的阻塞理论。我们认为$\mathcal X$在这里作为一个复杂的supermanifold本身的权利。本文的目的是证明，当$\mathcal X$是具有亏格$g>1$的$\mathcal S$的二级变形时：如果分裂$\mathcal X$的主要障碍类消失，则$\mathcal X$实际上是分裂的。这个结果自然地导致任何阶数的$\mathcal S$的奇变形的几何特征。
英文摘要：
An odd deformation of a super Riemann surface $\mathcal S$ is a deformation of $\mathcal S$ by variables of odd parity. In this article we study the obstruction theory of these odd deformations $\mathcal X$ of $\mathcal S$. We view $\mathcal X$ here as a complex supermanifold in its own right. Our objective in this article is to show, when $\mathcal X$ is a deformation of second order of $\mathcal S$ with genus $g>1$: if the primary obstruction class to splitting $\mathcal X$ vanishes, then $\mathcal X$ is in fact split. This result leads naturally to a conjectural characterisation of odd deformations of $\mathcal S$ of any order.
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