The structure of exceptional sequences on toric varieties of Picard rank two

Altmann, Klaus; Witt, Frederik

doi:10.48550/arxiv.2112.14637

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The Projective Bundle Of the Cotangent Bundle1

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2023

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“…For the toric case, Λ = K X , π * K P ℓ is admissible, cf. also [AW,Subsection (3.4)]. In this case, Pic(X)/Λ contains exactly rk K 0 (X) elements, so that an exceptional set of line bundles s is maximal if and only if φ Λ restricted to s is a bijection.…”

Section: The Projective Bundle Of the Cotangent Bundlementioning

confidence: 99%

Exceptional sequences of line bundles on projective bundles

Altmann¹,

Hochenegger²,

Witt³

2023

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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.

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Section: The Projective Bundle Of the Cotangent Bundlementioning

confidence: 99%