A counterexample to King's conjecture

[摘要] King's conjecture states that on every smooth complete toric variety $X$ there exists a strongly exceptional collection which generates the bounded derived category of $X$ and which consists of line bundles. We give a counterexample to this conjecture. This example is just the Hirzebruch surface $mathbb{F}_2$ iteratively blown up three times, and we show by explicit computation of cohomology vanishing that there exist no strongly exceptional sequences of length 7 which consist of line bundles.

[学科分类] 数学（综合）