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Izvestiya: Mathematics, 2013, Volume 77, Issue 5, Pages 1044–1065
DOI: https://doi.org/10.1070/IM2013v077n05ABEH002669 (Mi im7930) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Minimal Lefschetz decompositions of the derived categories for Grassmannians

A. Fonarev

M. V. Lomonosov Moscow State University
English version PDF (338 kB) Citations (15)
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DOI: https://doi.org/10.1070/IM2013v077n05ABEH002669
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.
Funding agency Grant number
Möbius Contest
Ministry of Education and Science of the Russian Federation 11.G34.31.0023
НШ-5139.2012.1
Russian Foundation for Basic Research 11-01-92613-KO-a
10-01-00678-a
Received: 18.10.2011
Revised: 17.01.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 5, Pages 203–224
DOI: https://doi.org/10.4213/im7930
Bibliographic databases:
Document Type: Article
UDC: 512.7+512.73
MSC: 14F05, 18E30
Language: English
Original paper language: Russian
Citation: A. Fonarev, “Minimal Lefschetz decompositions of the derived categories for Grassmannians”, Izv. RAN. Ser. Mat., 77:5 (2013), 203–224; Izv. Math., 77:5 (2013), 1044–1065
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:556
    Russian version PDF:250
    English version PDF:24
    References:58
    First page:36
     
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