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DERIVED CATEGORIES OF THE CAYLEY PLANE AND THE COADJOINT GRASSMANNIAN OF TYPE F

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Abstract

For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type E6, a full Lefschetz exceptional collection was constructed by Faenzi and Manivel. A general hyperplane section of the Cayley plane is the coadjoint Grassmannian of Dynkin type F4. We show that the restriction of the Faenzi–Manivel collection to such a hyperplane section gives a full Lefschetz exceptional collection, providing the first example of a full exceptional collection on a homogeneous variety of Dynkin type F.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    PIETER BELMANS

  2. Departement Wiskunde, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    PIETER BELMANS

  3. Algebraic Geometry Section, Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin str, Moscow, 119991, Russia

    ALEXANDER KUZNETSOV

  4. Laboratory of Algebraic Geometry, NRU HSE, Moscow, Russia

    ALEXANDER KUZNETSOV

  5. Institut für Mathematik, Universität Augsburg, Universitätsstr. 14, 86159, Augsburg, Germany

    MAXIM SMIRNOV

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  1. PIETER BELMANS
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  2. ALEXANDER KUZNETSOV
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  3. MAXIM SMIRNOV
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Correspondence to ALEXANDER KUZNETSOV.

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Pieter Belmans is partially supported by a postdoctoral fellowship from the Research Foundation-Flanders (FWO).

Alexander Kuznetsov is partially supported by the HSE University Basic Research Program.

Maxim Smirnov is partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 448537907.

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BELMANS, P., KUZNETSOV, A. & SMIRNOV, M. DERIVED CATEGORIES OF THE CAYLEY PLANE AND THE COADJOINT GRASSMANNIAN OF TYPE F. Transformation Groups 28, 9–34 (2023). https://doi.org/10.1007/s00031-021-09657-w

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