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Brill–Noether loci of rank 2 vector bundles on a general $\nu$-gonal curve


Authors: Youngook Choi, Flaminio Flamini and Seonja Kim
Journal: Proc. Amer. Math. Soc. 146 (2018), 3233-3248
MSC (2010): Primary 14H60, 14D20, 14J26
DOI: https://doi.org/10.1090/proc/14093
Published electronically: April 26, 2018
MathSciNet review: 3803651
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Abstract: In this paper we study the Brill Noether locus of rank 2, (semi)stable vector bundles with at least two sections and of suitable degrees on a general $\nu$-gonal curve. We classify its reduced components whose dimensions are at least the corresponding Brill–Noether number. We moreover describe the general member $\mathcal F$ of such components only in terms of extensions of line bundles with suitable minimality properties, providing information on the birational geometry of such components as well as on the very ampleness of $\mathcal F$.


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Additional Information

Youngook Choi
Affiliation: Department of Mathematics Education, Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea
MR Author ID: 709698
Email: ychoi824@yu.ac.kr

Flaminio Flamini
Affiliation: Dipartimento di Matematica, Universita’ degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica-00133 Roma, Italy
MR Author ID: 650600
Email: flamini@mat.uniroma2.it

Seonja Kim
Affiliation: Department of Electronic Engineering, Chungwoon University, Sukgol-ro, Nam-gu, Incheon, 22100, Republic of Korea
MR Author ID: 258121
Email: sjkim@chungwoon.ac.kr

Keywords: Stable rank-2 vector bundles, Brill–Noether loci, general $\nu$-gonal curves
Received by editor(s): February 3, 2017
Received by editor(s) in revised form: June 29, 2017, and September 15, 2017
Published electronically: April 26, 2018
Additional Notes: The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A3B03933342).
The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03930844).
Communicated by: Jerzy M. Weyman
Article copyright: © Copyright 2018 American Mathematical Society