Poincaré duality for tautological Chern subrings of orthogonal grassmannians - Karpenko, Nikita A.; Merkurjev, Alexander S. (MATHEMATICA SCANDINAVICA, 2022)
Let X be an orthogonal grassmannian of a nondegenerate quadratic form q over a field. Let C be the subring in the Chow ring CH(X) generated by the Chern classes of the tautological vector bundle on X. We prove Poincaré duality for C. For q of odd dimension, the result was already known due to an identification between C and the Chow ring of certain symplectic grassmannian. For q of even dimension, such an identification is not available.