In this paper, we compute the cohomology class of certain ‘special maximal‐rank loci’ originally defined by Aprodu and Farkas. By showing that such classes are non‐zero, we are able to verify the non‐emptiness portion of the Strong Maximal Rank Conjecture in a wide range of cases. As an application, we obtain new evidence for the existence portion of a well‐known conjecture due to Bertram, Feinberg and independently Mukai in higher rank Brill–Noether theory.

中文翻译：

---

强最大秩猜想和更高阶的Brill–Noether理论

在本文中，我们计算了最初由Aprodu和Farkas定义的某些“特殊最大秩基因座”的同调类。通过证明此类不是零，我们可以在很多种情况下验证强最大秩猜想的非空部分。作为一种应用，我们获得了有关高等Brill-Noether理论中Bertram，Feinberg和独立Mukai导致的一个著名猜想存在部分的新证据。