标题： 支持秩和所有哈塞特除子的交集 显示英文标题

标题： Supporting rank and the intersection of all Hassett Divisors

摘要： 我们证明所有特殊三次四维体的Hassett除子的交集$\mathcal Z$的维度是十六。 我们通过研究自然数的哪些子集$\mathbb N$可以作为正定整二次型的像获得，以及这种形式的最小可能秩是什么。 特别是，对于由所有可能的特殊三次四维体判别式的子集$\mathbb N$，我们证明这个秩是四，并且这是$\mathcal Z$在$\mathcal C$，即三次四维体的二十维模空间中的余维数。 显示英文摘要

摘要： We prove that the dimension of the intersection $\mathcal Z$ of all Hassett divisors of special cubic fourfolds is sixteen. We do this by studying which subsets of the natural numbers $\mathbb N$ can be obtained as the image of a positive-definite integral quadratic form and what the minimal possible rank of such a form is. In particular, for the subset of $\mathbb N$ consisting of all possible discriminants of special cubic fourfolds, we show this rank is four and that this is the codimension of $\mathcal Z$ in $\mathcal C$, the twenty-dimensional moduli space of cubic fourfolds.