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This article is cited in 16 scientific papers (total in 16 papers)
Minimal Lefschetz decompositions of the derived categories for Grassmannians
A. Fonarev M. V. Lomonosov Moscow State University
Abstract:
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, semi-orthogonal decompositions.
Received: 18.10.2011 Revised: 17.01.2012
Citation:
A. Fonarev, “Minimal Lefschetz decompositions of the derived categories for Grassmannians”, Izv. Math., 77:5 (2013), 1044–1065
Linking options:
https://www.mathnet.ru/eng/im7930https://doi.org/10.1070/IM2013v077n05ABEH002669 https://www.mathnet.ru/eng/im/v77/i5/p203
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Abstract page: | 604 | Russian version PDF: | 259 | English version PDF: | 38 | References: | 76 | First page: | 36 |
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