Algebraic Geometry Seminar: "The Genus of Space Curves and Derived Categories"

Abstract: A 19th-century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space. This is easy in the case of the projective plane but becomes quite involved already in the case of three-dimensional projective space. In this talk, I will give an introduction to the topic, introduce stability conditions in the derived category, and explain how the two can be related. From a modern perspective, there is no reason to restrict to the case of projective space, and I will discuss some recent progress on the question in the case of abelian threefolds in joint work with Emanuele Macri.

Host: Matt Kerr