NDLI: Residual categories for (co)adjoint Grassmannians in classical types

Content Provider	Scilit
Author	Kuznetsov, Alexander Smirnov, Maxim
Copyright Year	2021
Description	Journal: Compositio Mathematica 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.
Ending Page	1206
Starting Page	1172
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x21007090
Journal	Compositio Mathematica
Issue Number	6
Volume Number	157
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2021-05-20
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Residual categories for (co)adjoint Grassmannians in classical types