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    Exceptional collections on toric Fano threefolds and birational geometry

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    Bernardi and Tirabassi show the existence of full strong exceptional collections consisting of line bundles on smooth toric Fano 33-folds under assuming Bondal's conjecture, which states that the Frobenius push-forward of the structure sheaf \mc O_X generates the derived category Db(X)D^b(X) for smooth projective toric varieties XX. In this article, we show Bondal's conjecture for smooth toric Fano 33-folds and also improve their result, using birational geometry.Comment: 6 figure