Progress on syzygies of algebraic curves

Abstract

These lectures discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special emphasis on examples and explicit calculations. The notes are based on series of lectures given in Daejeon (March 2013), Rome (November-December 2015) and Guanajuato (February 2016).

arXiv comment24 pages, a few corrections. To appear in the Proceedings of the CIMPA-CIMAT-ICTP School on Moduli of Curves, 2016 (Lecture Notes in Mathematics)