On the derived category of the adjoint Grassmannian of type F

2021/07/16 by Smirnov, Maxim · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2107.07814

Abstract

We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type F₄. This gives the first example of a full exceptional collection on this variety and also completes the proof of a conjecture due to Alexander Kuznetsov and the author that relates the structure of the derived category of coherent sheaves to the small quantum cohomology in the case of adjoint varieties for non-simply laced groups.

Cited by

• Failure of Bott vanishing for (co)adjoint partial flag varieties
• Full exceptional collections on the isotropic Grassmannians

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