Brill–Noether theory of curves on 1 × 1 : tropical and classical approaches
Algebraic Combinatorics, Tome 2 (2019) no. 3, pp. 323-341.

The gonality sequence (d r ) r1 of a smooth algebraic curve comprises the minimal degrees d r of linear systems of rank r. We explain two approaches to compute the gonality sequence of smooth curves in 1 × 1 : 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]. The classical one extends the work [12] of Hartshorne on plane curves to curves on 1 × 1 .

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DOI : 10.5802/alco.47
Mots clés : gonality sequence, curves, bipartite graphs
Cools, Filip 1 ; D’Adderio, Michele 2 ; Jensen, David 3 ; Panizzut, Marta 4

1 KU Leuven Department of Mathematics Celestijnenlaan 200B B-3001 Heverle Belgium
2 Université Libre de Bruxelles (ULB) Département de Mathématique Boulevard du Triomphe B-1050 Bruxelles Belgium
3 University of Kentucky Department of Mathematics 719 Patterson Office Tower Lexington KY 40506-0027, USA
4 TU Berlin Institut für Mathematik Straße des 17. Juni 136 10623 Berlin Germany
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Cools, Filip; D’Adderio, Michele; Jensen, David; Panizzut, Marta. Brill–Noether theory of curves on $\protect \mathbb{P}^1 \times \protect \mathbb{P}^1$: tropical and classical approaches. Algebraic Combinatorics, Tome 2 (2019) no. 3, pp. 323-341. doi : 10.5802/alco.47. http://www.numdam.org/articles/10.5802/alco.47/

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