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Working paper

Residual categories for (co)adjoint Grassmannians in classical types

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