On minimal Lefschetz decompositions for Grassmannians

Details On minimal Lefschetz decompositions for Grassmannians On minimal Lefschetz decompositions for Grassmannians

2011-08-10

arxiv.org/abs/1108.2292v2

Mathematics

Algebraic Geometry

18 pages, 2 figures; v.2: minor corrections, to appear in Izvestiya RAN: Ser. Mat

Scientific paper

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 of them admit a Lefschetz basis consisting of equivariant vector bundles. We prove fullness of the first decomposition and conjecture it for the second one. In the case when $n$ and $k$ are coprime these decompositions coincide and are minimal. In general, we conjecture minimality of the second decomposition.

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