Abstract
For a nondegenerate quadratic form φ on a vector space V of dimension 2 n + 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 Ratajskiʼs characterization of the Chow ring of ( X 2 ) E , where E is a field extension splitting φ.
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