On the Chow groups of quadratic Grassmannians
In this text we get a description of the Chow-ring (modulo 2) of the Grassmanian of the middle-dimensional planes on arbitrary projective quadric. This is only a first step in the computation of the, so-called, generic discrete invariant of quadrics. This generic invariant contains the "splitting pattern" and "motivic decomposition type" invariants as specializations. Our computation gives an important invariant of the quadric Q. We formulate a conjecture describing the canonical dimension of Q in terms of .
Cite this article
A. Vishik, On the Chow groups of quadratic Grassmannians. Doc. Math. 10 (2005), pp. 111–130DOI 10.4171/DM/184