Free resolutions, or syzygies, with a graded structure are algebraic objects that encode many geometric properties. This correspondence lies at the heart of classical projective algebraic geometry. By analogy, multigraded resolutions should also provide powerful geometric tools. I will discuss some foundational results from the classical story and give an overview of recent work to extend these tools to the multigraded setting of toric geometry. This is joint work with Daniel Erman and Gregory G. Smith.
The geometry of toric syzygies
Christine Berkesch, University of Minnesota
2022 AWM Research Symposium