Simple helices on Fano threefolds

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dc.creatorPolishchuk, Alexander
dc.date2007-10-23
dc.date.accessioned2026-07-07T08:38:03Z
dc.date.available2026-07-07T08:38:03Z
dc.descriptionBuilding on the work of Nogin \cite{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.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0710.4195
dc.identifierhttp://arxiv.org/abs/0710.4195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140588
dc.subjectAlgebraic Geometry
dc.titleSimple helices on Fano threefolds
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