The signature of generalized flag manifolds and applications
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Let G be a linear algebraic group over ℂ and P be a parabolic subgroup. We determine the signatures of the flag manifold G/P. As an application, we prove that the nonsingular hypersurfaces of degree 2 in ℂP n are prime if n satisfies certain conditions.
KeywordsSignature flag manifold prime manifold
MR(2000) Subject Classification57T15 57R19
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