Exceptional collections on toric Fano threefolds and birational geometry

Details Exceptional collections on toric Fano threefolds and birational geometry Exceptional collections on toric Fano threefolds and birational geometry

2010-12-18

arxiv.org/abs/1012.4086v1

Mathematics

Algebraic Geometry

6 figures

Scientific paper

Bernardi and Tirabassi show the existence of full strong exceptional collections consisting of line bundles on smooth toric Fano $3$-folds under assuming Bondal's conjecture, which states that the Frobenius push-forward of the structure sheaf $\mc O_X$ generates the derived category $D^b(X)$ for smooth projective toric varieties $X$. In this article, we show Bondal's conjecture for smooth toric Fano $3$-folds and also improve their result, using birational geometry.

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