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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 5, Pages 203–224 (Mi izv7930)  

This article is cited in 6 scientific papers (total in 6 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.

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


DOI: https://doi.org/10.4213/im7930

Full text: PDF file (599 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:5, 1044–1065

Bibliographic databases:

Document Type: Article
UDC: 512.7+512.73
MSC: 14F05, 18E30
Received: 18.10.2011
Revised: 17.01.2012

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. W. Donovan, E. Segal, “Window shifts, flop equivalences and Grassmannian twists”, Compos. Math., 150:6 (2014), 942–978  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Fonarev, “Exceptional vector bundles on Grassmannians”, Russian Math. Surveys, 69:4 (2014), 768–770  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. E. Mayanskiy, “Poisson cohomology of two Fano threefolds”, J. Algebra, 424 (2015), 21–45  crossref  mathscinet  zmath  isi  scopus
    4. A. V. Fonarev, “On the Kuznetsov–Polishchuk conjecture”, Proc. Steklov Inst. Math., 290:1 (2015), 11–25  mathnet  crossref  crossref  isi  elib  elib
    5. W. Donovan, “Grassmannian twists, derived equivalences and brane transport”, String-Math 2012, Proc. Sympos. Pure Math., 90, eds. Donagi R., Katz S., Klemm A., Morrison D., Amer. Math. Soc., Providence, RI, 2015, 251–263  crossref  mathscinet  zmath  isi
    6. A. Kuznetsov, A. Perry, “Derived categories of cyclic covers and their branch divisors”, Selecta Math. (N.S.), 23:1 (2017), 389–423  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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