The Strong Maximal Rank conjecture and higher rank Brill–Noether theory

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,...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2021-07, Vol.104 (1), p.169-205
Main Authors: Cotterill, Ethan, Alonso Gonzalo, Adrián, Zhang, Naizhen
Format: Article
Language:English
Subjects:
05E05
05E10 (secondary)
14H51
14H60 (primary)
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Summary: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12427