Exceptional sequences of line bundles on projective bundles - Altmann, Klaus; Hochenegger, Andreas; Witt, Frederik (MATHEMATICA SCANDINAVICA, 2025)
For a vector bundle $\mathcal {E}→ \mathbb {P}^\ell $ we investigate exceptional sequences of line bundles on the total space of the projectivisation $X=\mathbb {P}(\mathcal {E})$. In particular, we consider the case of the cotangent bundle of $\mathbb {P}^\ell $. If $\ell =2$, we completely classify the (strong) exceptional sequences and show that any maximal exceptional sequence is full. For general $\ell $, we prove that the Rouquier dimension of $\mathcal {D}(X)$ equals $\dim X$, thereby confirming a conjecture of Orlov.