Exceptional sequences of line bundles on projective bundles
Klaus Altmann, Andreas Hochenegger, Frederik Witt

TL;DR
This paper classifies exceptional line bundle sequences on projective bundles, especially for cotangent bundles of projective spaces, and confirms a conjecture relating Rouquier dimension to the dimension of the total space.
Contribution
It provides a complete classification of exceptional sequences for certain projective bundles and proves the Rouquier dimension equals the dimension of the total space for general cases.
Findings
Complete classification for $ ext{dim}( ext{base})=2$
Any maximal exceptional sequence is full in this case
Rouquier dimension equals the dimension of the total space for general $ ext{dim}( ext{base})$
Abstract
For a vector bundle we investigate exceptional sequences of line bundles on the total space of the projectivisation . In particular, we consider the case of the cotangent bundle of . If , we completely classify the (strong) exceptional sequences and show that any maximal exceptional sequence is full. For general , we prove that the Rouquier dimension of equals , thereby confirming a conjecture of Orlov.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Neuroimaging Techniques and Applications · Homotopy and Cohomology in Algebraic Topology
