Exceptional sequences of line bundles on projective bundles

Abstract

For a vector bundle E → P ℓ we investigate exceptional sequences of line bundles on the total space of the projectivisation X = P(E). In particular, we consider the case of the cotangent bundle of P ℓ . If ℓ = 2, we will completely classify the (strong) exceptional sequences and show that any maximal exceptional sequence is full. For general ℓ, we prove that the Rouquier dimension of D(X) equals dim X, thereby confirming a conjecture of Orlov.