Bryant G. Mathews: Incompressibility of orthogonal Grassmannians of rank 2

Submission: 2009, Feb 27

For a nondegenerate quadratic form phi on a vector space V of dimension 2n + 1, let X_d be the variety of d-dimensional totally isotropic subspaces of V. We give a sufficient condition for X_2 to be 2-incompressible, generalizing in a natural way the known sufficient conditions for X_1 and X_n. 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 (X_2)_E, where E is a =0Cfield extension splitting phi.

2000 Mathematics Subject Classification: 11E04; 14C25

Keywords and Phrases: canonical dimension, incompressibility, projective homogeneous varieties, quadratic forms, higher Witt indices, correspondences, Pieri-type formulas

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