## Algebraic Geometry Seminar

Howard Nuer

Northeastern University

Relative Bridgeland stability conditions with applications to cubic fourfolds and generalized DT invariants

**Abstract:**A foundational tool in the study of families of Bridgeland semistable objects on a fixed variety is the notion of a constant sheaf of t-structures pioneered by Abramovich and Polishchuk. However, throughout algebraic geometry it is often useful to be able to deform the underlying variety to make the objects of study more tractable. In joint work with Lahoz, Macri, and Perry we develop a tool for studying how Bridgeland stability varies under such deformations to allow for the use of such techniques in Bridgeland stability. Although quite technical in full detail, we hope to share the general ideas involved in these so-called “relative Bridgeland stability conditions.” Instead of going into all of the details, we will cover in more detail two important applications of our tool. The first (which depends on some joint work with Bayer and Stellari as well as the above authors) is to proving the full version of Addington and Thomas’s equivalence between a cubic fourfold having an associated K3 surface in the hodge theoretic sense (due to Hassett) and having one in the derived category sense (due to Kuznetsov). The second is to the deformation invariance of Toda’s generalized DT invariants.

Wednesday March 1, 2017 at 5:00 PM in SEO 427