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 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.
Exceptional sequences of line bundles on projective bundles
A. Hochenegger;
2025-01-01
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 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.File in questo prodotto:
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Hochenegger_eprint.pdf
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