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

par Cools, Filip;D'Adderio, Michele ;Jensen, David;Panizzut, Marta
Référence Algebraic combinatorics, 2, 3, page (323-341)
Publication Publié, 2019

Article révisé par les pairs

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Résumé :

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]. The classical one extends the work [12] of Hartshorne on plane curves to curves on P1 × P1