| Abstract |
Koszul modules offer a powerful framework for studying the syzygies of algebraic varieties and the geometry of special divisors on moduli spaces. Associated with a subspace in a second exterior power, the Koszul module encodes the syzygies of the exterior algebra, yielding direct applications to syzygies of canonical curves, vector bundle theory, and hyperplane arrangements.
In this two-part seminar based on joint works with G. Farkas, Y. Kim, C. Raicu, C. Spiridon and J. Weyman, we present the geometric machinery of Koszul modules and their applications to the geometry of curves and projective varieties:
Part II: Resonance loci and Vector Bundles. We explore the deep connection between Koszul modules, resonance loci, and vector bundles on algebraic curves and projective varieties. We review Mukai's model in genus 8 through the lens of Koszul modules. |
