# Progress on syzygies of algebraic curves

## TL;DR

This paper reviews recent progress on the syzygies of algebraic curves, focusing on conjectures like Green, Prym-Green, and Green-Lazarsfeld Secant, using geometric and variational methods with explicit examples.

## Contribution

It provides an overview of recent advances and methods in understanding syzygies of algebraic curves, emphasizing geometric and explicit computational approaches.

## Key findings

- Progress on Green conjecture for generic curves
- Verification of Prym-Green conjecture in specific cases
- Development of geometric and variational techniques

## 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).