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On the derived category of the Cayley plane II


Authors: Daniele Faenzi and Laurent Manivel
Journal: Proc. Amer. Math. Soc. 143 (2015), 1057-1074
MSC (2010): Primary 14F05, 14J60, 14M17
DOI: https://doi.org/10.1090/S0002-9939-2014-12312-4
Published electronically: November 4, 2014
MathSciNet review: 3293722
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Abstract: We find a full strongly exceptional collection for the Cayley plane $ \mathbb{O}\mathbb{P}^2$, the simplest rational homogeneous space of the exceptional group $ E_6$. This collection, closely related to the one given by the second author in 2011, consists of $ 27$ vector bundles which are homogeneous for the group $ E_6$, and is a minimal Lefschetz collection with respect to the minimal equivariant embedding of $ \mathbb{O}\mathbb{P}^2$.


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Additional Information

Daniele Faenzi
Affiliation: Université de Pau et des Pays de l’Adour, Avenue de l’Université, BP 576, 64012 PAU Cedex, France
Address at time of publication: Université de Bourgogne, Institut de Mathématiques de Bourgogne, CNRS-UMR 5584, 9 Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France.
Email: daniele.faenzi@univ-pau.fr, daniele.faenzi@u-bourgogne.fr

Laurent Manivel
Affiliation: Université de Grenoble, BP 74, 38402 Saint-Martin d’Hères, France
Address at time of publication: UMI 3457 CNRS/Centre de Recherches Mathémathiques, Université de Montréal, Pavillon André-Aisenstadt, 2920 Chemin de la Tour, Montréal, Québec, H3T 1J4, Canada
Email: laurent.manivel@ujf-grenoble.fr, laurent.manivel@math.cnrs.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-12312-4
Keywords: Cayley plane, derived category, full strongly exceptional collection
Received by editor(s): February 24, 2012
Received by editor(s) in revised form: October 30, 2012, April 4, 2013, and July 22, 2013
Published electronically: November 4, 2014
Additional Notes: The first author was partially supported by ANR projects INTERLOW ANR-09-JCJC-0097-0 and GEOLMI ANR-11-BS03-0011
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society

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