The gonality sequence of a smooth algebraic curve comprises the minimal degrees of linear systems of rank . We explain two approaches to compute the gonality sequence of smooth curves in : 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 .
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DOI: 10.5802/alco.47
Cools, Filip 1; D’Adderio, Michele 2; Jensen, David 3; Panizzut, Marta 4
@article{ALCO_2019__2_3_323_0, author = {Cools, Filip and D{\textquoteright}Adderio, Michele and Jensen, David and Panizzut, Marta}, title = {Brill{\textendash}Noether theory of curves on $\protect \mathbb{P}^1 \times \protect \mathbb{P}^1$: tropical and classical approaches}, journal = {Algebraic Combinatorics}, pages = {323--341}, publisher = {MathOA foundation}, volume = {2}, number = {3}, year = {2019}, doi = {10.5802/alco.47}, zbl = {07066877}, mrnumber = {3968740}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.47/} }
TY - JOUR AU - Cools, Filip AU - D’Adderio, Michele AU - Jensen, David AU - Panizzut, Marta TI - Brill–Noether theory of curves on $\protect \mathbb{P}^1 \times \protect \mathbb{P}^1$: tropical and classical approaches JO - Algebraic Combinatorics PY - 2019 SP - 323 EP - 341 VL - 2 IS - 3 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.47/ DO - 10.5802/alco.47 LA - en ID - ALCO_2019__2_3_323_0 ER -
%0 Journal Article %A Cools, Filip %A D’Adderio, Michele %A Jensen, David %A Panizzut, Marta %T Brill–Noether theory of curves on $\protect \mathbb{P}^1 \times \protect \mathbb{P}^1$: tropical and classical approaches %J Algebraic Combinatorics %D 2019 %P 323-341 %V 2 %N 3 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.47/ %R 10.5802/alco.47 %G en %F ALCO_2019__2_3_323_0
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, Volume 2 (2019) no. 3, pp. 323-341. doi : 10.5802/alco.47. https://alco.centre-mersenne.org/articles/10.5802/alco.47/
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