An introduction to Boij-Söderberg theory
Abstract: A major theme in algebraic geometry is to study an embedded projective variety X via the minimal free resolution of its coordinate ring C[X]. Such a resolution linearizes the complex multiplicative structure of the coordinate ring, making it easier to analyze. The first fundamental result in this area is the Hilbert syzygy theorem, which gives a simple bound on the maximal length of a minimal free resolution. In general, structural results on minimal free resolutions are very difficult to obtain. We will introduce some open problems in this area and discuss the relatively modern results of Boij-Söderberg theory, which offer surprising numerical constraints on minimal free resolutions.