Séminaire de Géométrie Complexe
# Maximal Brill-Noether loci

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salle 207 bâtiment 1R2 (Institut de Mathématiques de Toulouse)
### salle 207 bâtiment 1R2

#### Institut de Mathématiques de Toulouse

Description

Brill-Noether theory answers the question of whether a general curve of genus g admits a degree d map to projective space P^r. A refined Brill-Noether theory hopes to answer the question of whether a "general" curve of genus g and degree d in P^r admits a a degree e map to P^s . In other words, we want to know about the relative position between Brill-Noether loci in the moduli space of curves. I'll explain a strategy for distinguishing Brill-Noether loci by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill-Noether loci with respect to containment. Via an analysis of the stability of Lazarsfeld-Mukai bundles, we obtain new lifting results for linear systems of rank 3 which suffice to prove the maximal Brill-Noether loci conjecture in genus 9-19, 22, and 23. This is joint work with Richard Haburcak.