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：

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强最大秩猜想和更高秩的 Brill-Noether 理论

在本文中，我们计算了最初由 Aprodu 和 Farkas 定义的某些“特殊最大秩位点”的上同调类。通过证明这些类是非零的，我们能够在各种情况下验证强最大秩猜想的非空部分。作为应用，我们获得了由 Bertram、Feinberg 和独立的 Mukai 在更高阶的 Brill-Noether 理论中引起的著名猜想的存在部分的新证据。