Geodesic
Minimal Lefschetz decompositions of the derived categories for Grassmannians
Izvestiya. Mathematics , Tome 77 (2013) no. 5, pp. 1044-1065.

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We construct two Lefschetz decompositions of the derived category of coherent sheaves on the Grassmannian of $k$-dimensional subspaces in a vector space of dimension $n$. Both decompositions admit a Lefschetz basis consisting of equivariant vector bundles. We prove that the first decomposition is full. In the case when $n$ and $k$ are coprime, the decompositions coincide and are minimal. We conjecture that the second decomposition is always full and minimal.
Keywords: derived categories of coherent sheaves
Mots-clés : semi-orthogonal decompositions. 
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A. Fonarev. Minimal Lefschetz decompositions of the derived categories for Grassmannians. Izvestiya. Mathematics , Tome 77 (2013) no. 5, pp. 1044-1065. http://geodesic.mathdoc.fr/item/IM2_2013_77_5_a6/

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