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Simple Helices on Fano Threefolds

Published online by Cambridge University Press:  20 November 2018

A. Polishchuk
A. Polishchuk*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97405, U.S.A. e-mail: [email protected]
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Abstract

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Building on the work of Nogin, we prove that the braid group ${{B}_{4}}$ acts transitively on full exceptional collections 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 (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds with ${{b}_{2}}\,=\,1$ and very ample anticanonical class, every exceptional coherent sheaf is locally free.

Keywords

14F0514J45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 520 - 526
Copyright
Copyright © Canadian Mathematical Society 2011

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