Derived Categories of the Cayley Plane and the Coadjoint Grassmannian of Type F

In our previous paper we suggested a conjecture relating the structure of the small quantum cohomology ring of a smooth Fano variety of Picard number 1 to the structure of its derived category of coherent sheaves. Here we generalize this conjecture, make it more precise, and support it by the examples of (co)adjoint homogeneous varieties of simple algebraic groups of Dynkin types $\mathrm {A}_n$ and $\mathrm {D}_n$ , that is, flag varieties $\operatorname {Fl}(1,n;n+1)$ and isotropic orthogonal Grassmannians $\operatorname {OG}(2,2n)$ ; in particular, we construct on each of those an exceptional collection invariant with respect to the entire automorphism group. For $\operatorname {OG}(2,2n)$ this is the first exceptional collection proved to be full.

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Derived categories of Grassmannians: a survey

Fonarev

2024

Успехи математических наук

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Derived Categories of the Cayley Plane and the Coadjoint Grassmannian of Type F

Cited by 3 publications

References 22 publications

Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold

Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold

Residual categories for (co)adjoint Grassmannians in classical types

Derived categories of Grassmannians: a survey

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