Katsura and Oort obtained an explicit description of the supersingular locus ${\mathcal{S}}_{3,1}$ of the Siegel modular variety of degree 3 in terms of class numbers. In this paper we study an alternative stratification of ${\mathcal{S}}_{3,1}$, the so-called mass stratification. We show that when $p\ne 2$, there are eleven strata (one of a-number 3, two of a-number 2 and eight of a-number 1). We give an explicit mass formula for each stratum and classify possible automorphism groups on each stratum of a-number one. On the largest open stratum we show that every automorphism group is $\{\pm 1\}$ if and only if $p\ne 2$; that is, we prove that Oort's conjecture on the automorphism groups of generic supersingular abelian threefolds holds precisely when $p>2$.

Katsura 和 Oort 获得了超奇异轨迹的明确描述 ${\mathcal{秒}}_{3,1}$就类数而言，Siegel 模块化变体的程度为 3。在本文中，我们研究了另一种分层${\mathcal{秒}}_{3,1}$，所谓的群众分层。我们证明当$磷\ne 2$中，有11地层（之一一-number 3中，两个的一个的-number 2和八个一个-number 1）。我们给每个阶层明确的质量公式和各阶层分类可能构群一-值之一。在最大的开放层上，我们证明每个自同构群都是$\{\pm 1\}$ 当且仅当 $磷\ne 2$; 也就是说，我们证明了奥尔特关于泛型超奇异阿贝尔三重自同构群的猜想在$磷>2$.