Brill–Noether theory of curves on P1 × P1: Tropical and classical approaches

Filip Cools; Michele D’Adderio; David Jensen; Marta Panizzut

doi:10.5802/ALCO.47

Brill–Noether theory of curves on P¹ × P¹: Tropical and classical approaches

Filip Cools
, Michele D’Adderio
, David Jensen
, Marta Panizzut

Mathematics

Producción científica: Article › revisión exhaustiva

5 Citas (Scopus)

Resumen

The gonality sequence (dr)_r>₁ of a smooth algebraic curve comprises the minimal degrees dr of linear systems of rank r. We explain two approaches to compute the gonality sequence of smooth curves in P¹ ×P¹: a tropical and a classical approach. The tropical approach uses the recently developed Brill–Noether theory on tropical curves and Baker’s specialization of linear systems from curves to metric graphs [1].

Idioma original	English
Páginas (desde-hasta)	323-341
Número de páginas	19
Publicación	Algebraic Combinatorics
Volumen	2
N.º	3
DOI	https://doi.org/10.5802/ALCO.47
Estado	Published - 2019

Nota bibliográfica

Publisher Copyright:
© The journal and the authors, 2019.

Financiación

Acknowledgements. Marta Panizzut is supported by the Einstein Foundation Berlin.

Financiadores
Einstein Stiftung Berlin

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Acceder al documento

10.5802/ALCO.47

Otros archivos y enlaces

Citar esto

@article{2d6064a2f40d47b89227243a0169eafb,

title = "Brill–Noether theory of curves on P1 × P1: Tropical and classical approaches",

abstract = "The gonality sequence (dr)r>1 of a smooth algebraic curve comprises the minimal degrees dr of linear systems of rank r. We explain two approaches to compute the gonality sequence of smooth curves in P1 ×P1: a tropical and a classical approach. The tropical approach uses the recently developed Brill–Noether theory on tropical curves and Baker{\textquoteright}s specialization of linear systems from curves to metric graphs [1].",

keywords = "Bipartite graphs, Curves, Gonality sequence",

author = "Filip Cools and Michele D{\textquoteright}Adderio and David Jensen and Marta Panizzut",

note = "Publisher Copyright: {\textcopyright} The journal and the authors, 2019.",

year = "2019",

doi = "10.5802/ALCO.47",

language = "English",

volume = "2",

pages = "323--341",

journal = "Algebraic Combinatorics",

issn = "2589-5486",

publisher = "Combinatorics Consortium",

number = "3",

}

TY - JOUR

T1 - Brill–Noether theory of curves on P1 × P1

T2 - Tropical and classical approaches

AU - Cools, Filip

AU - D’Adderio, Michele

AU - Jensen, David

AU - Panizzut, Marta

N1 - Publisher Copyright: © The journal and the authors, 2019.

PY - 2019

Y1 - 2019

N2 - The gonality sequence (dr)r>1 of a smooth algebraic curve comprises the minimal degrees dr of linear systems of rank r. We explain two approaches to compute the gonality sequence of smooth curves in P1 ×P1: a tropical and a classical approach. The tropical approach uses the recently developed Brill–Noether theory on tropical curves and Baker’s specialization of linear systems from curves to metric graphs [1].

AB - The gonality sequence (dr)r>1 of a smooth algebraic curve comprises the minimal degrees dr of linear systems of rank r. We explain two approaches to compute the gonality sequence of smooth curves in P1 ×P1: a tropical and a classical approach. The tropical approach uses the recently developed Brill–Noether theory on tropical curves and Baker’s specialization of linear systems from curves to metric graphs [1].

KW - Bipartite graphs

KW - Curves

KW - Gonality sequence

UR - https://www.scopus.com/pages/publications/85093395789

UR - https://www.scopus.com/pages/publications/85093395789#tab=citedBy

U2 - 10.5802/ALCO.47

DO - 10.5802/ALCO.47

M3 - Article

AN - SCOPUS:85093395789

SN - 2589-5486

VL - 2

SP - 323

EP - 341

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 3

ER -