| 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 I: Koszul Modules, Scheme Structure, and Reducedness. We introduce the construction of Koszul modules and their support loci. We focus on the scheme structure of resonance schemes and the key linear algebra conditions that ensure the reducedness of the associated resonance schemes and the finiteness of the Koszul modules. |
