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Apr 27 at 11:10 comment added user45397 Thank you for the extra hints.
Apr 27 at 10:47 comment added Chris H I'm not sure of a specific reference for this, but any source on Schubert varieties explains their stratification into affine spaces. For computing the cohomology, it's just the computation of cellular cohomology when all (CW) cells are even dimensional, this is explained in any algebraic topology text, eg, Hatcher's Algebraic topology.
Apr 27 at 6:49 comment added user45397 Thank you so much for the answer! I am not quite familiar with the Betti number computations using affine stratification. Could you please add a reference in the comment so that I can understand the computation better?
Apr 27 at 5:35 vote accept user45397
Apr 26 at 21:45 history answered Chris H CC BY-SA 4.0