On the full, strongly exceptional collections on toric varieties with Picard number three

Abstract

We investigate full strongly exceptional collections on smooth, com- plete toric varieties. We obtain explicit results for a large family of varieties with Picard number three, containing many of the families already known. We also describe the relations between the collections and the split of the push forward of the trivial line bundle by the toric Frobenius morphism.

References in corpus (4)

• Maximal lengths of exceptional collections of line bundles
• Examples for exceptional sequences of invertible sheaves on rational surfaces
• Family of counterexamples to King's conjecture
• Derived category of toric varieties with Picard number three

Cited by in corpus (14)

• Resolutions of toric subvarieties by line bundles and applications
• A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
• A note on the Frobenius morphism on toric varieties
• Derived category of toric fibrations
• Exceptional collections on toric Fano threefolds and birational geometry
• On Landau-Ginzburg Systems and ${\mathcal{D}}^b(X)$ of projective bundles
• Derived Category of Fibrations
• f-vectors implying vertex decomposability
• Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two
• On Landau-Ginzburg systems and ${\mathcal{D}}^b(X)$ of various toric Fano manifolds with small picard group
• Equivalent condition for approximately Cohen-Macaulay complexes
• Strong full exceptional collections on certain toric varieties with Picard number three via mutations
• Hilbert-Kunz functions of a Hirzebruch surface
• Selected topics on Toric Varieties