Poincaré duality for tautological Chern subrings of orthogonal grassmannians
DOI:
https://doi.org/10.7146/math.scand.a-132376Abstract
Let $X$ be an orthogonal grassmannian of a nondegenerate quadratic form $q$ over a field. Let $C$ be the subring in the Chow ring $\text {CH}(X)$ 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.
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