Lectures on the Syzygies and Geometry of Algebraic Varieties

Over the past forty years, a substantial body of work has appeared centered around the syzygies of algebraic varieties. Classical results about defining equations have emerged as the first cases of a much more general picture involving higher syzygies. Moreover, as computer-assisted computations have become practical, Castelnuovo-Mumford regularity has come into focus as a measure of algebraic complexity. This research has touched on a wide array of topics in algebraic geometry, and the time …