Angela Ortega

HIGHER RANK BRILL–NOETHER THEORY ON SECTIONS OF K3 SURFACES

We discuss the role of K3 surfaces in the context of Mercats conjecture in higher rank Brill-Noether theory. Using liftings of Koszul classes, we show that Mercats conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether-Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercats conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercats conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier-Mukai involution on the moduli space M_{11}.

The Brill–Noether curve and Prym-Tyurin varieties

We prove that the Jacobian of a general curve C of genus

The Prym map of degree-7 cyclic coverings

g=2a+1

The uniformization of the moduli space of principally polarized abelian 6-folds

, with

On the moduli space of rank 3 vector bundles on a genus 2 curve and the Coble cubic

a\ge 2

Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

, can be realized as a Prym-Tyurin variety for the Brill–Noether curve