Simple Helices on Fano Threefolds

Canadian mathematical bulletin

A. Polishchuk¹ 

[1]Department of Mathematics, University of Oregon, Eugene, OR 97405, U.S.A.

关键词: turning point;    singularity;    Sturm-Liouville;    infinite products;    Hadamard's theorem;    eigenvalues;   

DOI  :  10.4153/CMB-2010-106-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Building on the work of Nogin,we prove that the braid group $B_4$ acts transitively on full exceptionalcollections of vector bundles on Fano threefolds with $b_2=1$ and$b_3=0$. Equivalently,this group acts transitively on the set of simple helices (consideredup to a shift in the derived category) on such a Fano threefold. Wealso prove that onthreefolds with $b_2=1$ and very ample anticanonical class, everyexceptional coherentsheaf is locally free.

【 授权许可】

Unknown