Lefschetz exceptional collections in S_k-equivariant categories of (P^n)^k

Abstract

We consider the bounded derived category D_S_k(X^n_k) of S_k-equivariant coherent sheaves on (P^n)^k. One of the ways to describe derived category is via an exceptional collection. We consider a special class of exceptional collections - Lefschetz exceptional collections. The goal of the dissertation is to construct in the category D_S_k(X^n_k) a rectangular Lefschetz exceptional collection when this is possible, or a minimal Lefschetz exceptional collection when a rectangular one does not exist.The main results of the dissertation include the construction of a rectangular Lefschetz exceptional collection in the case k= 3 and in the case n= 1 when gcd(n+1,k) = 1. We also construct minimal Lefschetz exceptional collection for n= 1 and even k, and for n= 2 and k= 3.--Author's abstract