Residual categories for (co)adjoint Grassmannians in classical types
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.04148
 Bibcode:
 2020arXiv200104148K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory;
 Mathematics  Symplectic Geometry
 EPrint:
 31 pages