Lefschetz exceptional collections in 𝑆𝑘 -equivariant categories of (ℙ𝑛)𝑘

Mikhail Mironov

Abstract: We consider the bounded derived category of 𝑆𝑘-equivariant coherent sheaves on (ℙ𝑛)𝑘. The goal of this paper is to construct in this category a rectangular Lefschetz exceptional collection of maximal length when this is possible, or a minimal Lefschetz exceptional collection when a rectangular one does not exist. The main results of the paper include the construction of a full rectangular Lefschetz exceptional collection in the case 𝑘=3 and in the case 𝑛=1 when gcd(𝑛+1,𝑘)=1. We also construct a full minimal Lefschetz exceptional collection for 𝑛=1 and even k, and for 𝑛=2 and 𝑘=3