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Expected dimensions of higher-rank Brill-Noether loci


Author: Naizhen Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 3735-3746
MSC (2010): Primary 14D20, 14H10, 14H51, 14H60
DOI: https://doi.org/10.1090/proc/13542
Published electronically: March 23, 2017
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Abstract: In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also leads to a new and much simpler proof of a theorem in his 2015 work. Our result generalizes the well-known result by Bertram, Feinberg and independently Mukai on expected dimension of rank two Brill-Noether loci with canonical determinant and partially verifies a conjecture (in rank two) of Grzegorczyk and Newstead on coherent systems.


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Additional Information

Naizhen Zhang
Affiliation: Department of Mathematics, University of California, Davis, One Shields Avenue, Davis, California 95616
Email: nzhzhang@math.ucdavis.edu

DOI: https://doi.org/10.1090/proc/13542
Received by editor(s): October 26, 2015
Received by editor(s) in revised form: July 28, 2016, and October 11, 2016
Published electronically: March 23, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 Retained by the author

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