## On the Chow groups of quadratic Grassmannians

### Summary

Summary: 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 $J(Q)$ of the quadric Q. We formulate a conjecture describing the canonical dimension of Q in terms of $J(Q)$.

### Mathematics Subject Classification

11E04, 14C15, 14M15

### Keywords/Phrases

quadrics, Chow groups, grassmannians, Steenrod operations