Geodesic
Simple Helices on Fano Threefolds
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 520-526

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DOI

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.
DOI : 10.4153/CMB-2010-106-x
Mots-clés : 14F05, 14J45 
Polishchuk, A. Simple Helices on Fano Threefolds. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 520-526. doi: 10.4153/CMB-2010-106-x
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     doi = {10.4153/CMB-2010-106-x},
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