Time: March 12, 2024, 2:00 pm

Place: Room 403, IMI – BAS

Speaker: Morgan Brown  (University of Miami)

Title: The Cox ring perspective on birational geometry

Further information:

Abstract. The Mori program for birational classification of algebraic varieties attempts to classify algebraic varieties by producing canonical models, polarized by the canonical class. This is accomplished through a series of algebraic surgery operations, such as flips, flops, and divisorial contractions. A complementary viewpoint is that of the total coordinate ring or Cox ring. Here birational maps are understood by looking at the totality of all linear series on the variety, endowed with a ring structure directly analogous to that of the homogeneous coordinate ring of a projective variety. I will give an overview of how Cox rings can help clarify many phenomena in birational geometry.