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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 17, Issue 1


Invariants of the Brill–Noether curve

Abel Castorena
  • Centro de Ciencias Matemáticas, Unidad Morelia, Universidad Nacional Autónoma de México, Apartado Postal 61-3 (Xangari), 58089 Morelia, Michoacán, Mexico
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/ Alberto López Martín
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  • Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 100, Jardim Botânico, Rio de Janeiro, RJ 22460-902, Brazil
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/ Montserrat Teixidor i Bigas
Published Online: 2017-02-17 | DOI: https://doi.org/10.1515/advgeom-2016-0027


For a projective nonsingular curve of genus g, the Brill–Noether locus Wdr(C) parametrizes line bundles of degree d over C with at least r + 1 (linearly independent) sections. When the curve is generic and the Brill–Noether number ρ(g, r, d) equals 1, one can then talk of the Brill–Noether curve. We introduce combinatorial methods that, with help from the theory of limit linear series, allow us to find invariants of Brill–Noether loci. In particular, we explore the first two invariants of the Brill–Noether curve, giving a new way of calculating the genus of this curve and computing its gonality when C has genus 5.

Kwywords: Brill–Noether curve; limit linear series; genus

MSC 2010: Primary 14H60; Secondary 14H51; 05E15

Communicated by: I. Coskun


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About the article

Received: 2014-12-28

Revised: 2015-06-26

Published Online: 2017-02-17

Published in Print: 2017-01-01

Citation Information: Advances in Geometry, Volume 17, Issue 1, Pages 39–52, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0027.

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Abel Castorena, Alberto López Martín, and Montserrat Teixidor i Bigas
Journal of Pure and Applied Algebra, 2017

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