Exceptional collections on toric Fano threefolds and birational geometry
Exceptional collections on toric Fano threefolds and birational geometry
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DOI：
10.1142/s0129167x14500724
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发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
Hokuto Uehara
中科院分区：
文献类型：
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作者：
Hokuto Uehara
Bernardi和Tirabassi证明了在Bondal猜想的假设下，光滑复曲面Fano $3$-folds上存在由线丛组成的完全强例外集，该猜想指出结构层$\mc O_X$的Frobenius推进生成光滑投射复曲面簇$X$的导出范畴$D^B（X）$。本文利用双有理几何证明了光滑复曲面Fano $3$-折叠的Bondal猜想，并改进了他们的结果。
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.