University of Sydney Algebra Seminar

Tyler L. Kelly

Friday 27 February, 12-1pm, in Carslaw 175

Kuznetsov Categories for Gauged Linear Sigma Models

The derived category of coherent sheaves on a variety \(X\) is a robust algebraic invariant of a variety, holding a wealth of information. For certain Fano varieties, the derived category has very interesting admissible subcategories that hold the majority of the geometric information. For example, Kuznetsov identified a component of the derived category of the cubic fourfold that looks much like the derived category of a K3 surface, and used this information to identify interesting geometry about the cubic fourfold. This subcategory and some other examples of the same phenomenon are now called Kuznetsov components of the derived category. Unfortunately, the Kuznetsov component has not been given a uniform definition. In this talk, we propose a definition of a Kuznetsov category for a gauged linear sigma model, an equivariant curved variant of the derived category. This definition allows us to create new study of it. We then provide some results that help justify our definition. This is joint work with David Favero and Dan Kaplan.