Incompressibility of orthogonal Grassmannians of rank 2
Abstract
For a nondegenerate quadratic form phi on a vector space V of dimension 2n + 1, let Xd be the variety of d-dimensional totally isotropic subspaces of V. We give a sufficient condition for X2 to be 2-incompressible, generalizing in a natural way the known sufficient conditions for X1 and Xn. Key ingredients in the proof include the Chernousov-Merkurjev method of motivic decomposition as well as Pragacz and Ratajski's characterization of the Chow ring of (X2)E, where E is a field extension splitting phi.
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