Strong exceptional sequences of vector bundles on certain Fano varieties

In an unpublished preprint, A. King conjectured that there are tilting bundles over projective varieties which are obtained as invariant quotients of affine spaces for linear actions of reductive groups. The goal of this paper is to give further examples of strong exceptional sequences of vector bundles on certain projective varieties. These are obtained as geometric invariant quotients of affine spaces by linear actions of reductive groups, as in King’s conjecture.