Details
| Original language | English |
|---|---|
| Pages (from-to) | 169-205 |
| Number of pages | 37 |
| Journal | Journal of the London Mathematical Society |
| Volume | 104 |
| Issue number | 1 |
| Early online date | 13 Jan 2021 |
| Publication status | Published - Jul 2021 |
Abstract
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.
Keywords
- 05E05, 05E10 (secondary), 14H51, 14H60 (primary)
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Journal of the London Mathematical Society, Vol. 104, No. 1, 07.2021, p. 169-205.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Strong Maximal Rank conjecture and higher rank Brill–Noether theory
AU - Cotterill, Ethan
AU - Alonso Gonzalo, Adrián
AU - Zhang, Naizhen
N1 - Funding Information: We are grateful to Wouter Castryck, Renzo Cavalieri, Marc Coppens, Joe Harris, Thomas Lam, Alex Massarenti, Brian Osserman, and Richard Stanley for useful comments and conversations. Special thanks are due to Peter Newstead and Montserrat Teixidor i Bigas for the detailed corrections and suggestions they provided after reading an earlier version of this paper. Finally, we are grateful for the CNPq postdoctoral scheme that allowed the first and third authors to meet; and to the anonymous referee, who flagged several errors and whose suggestions have helped improve the organization and quality of exposition.
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - 05E05
KW - 05E10 (secondary)
KW - 14H51
KW - 14H60 (primary)
UR - http://www.scopus.com/inward/record.url?scp=85099333136&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1906.07618
DO - 10.48550/arXiv.1906.07618
M3 - Article
AN - SCOPUS:85099333136
VL - 104
SP - 169
EP - 205
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 1
ER -