GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS

Abstract

AbstractGroebner bases for the ideals determining mod$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2$cohomology of the real flag manifolds$F(1,1,n)$and$F(1,2,n)$are obtained. These are used to compute appropriate Stiefel–Whitney classes in order to establish some new nonembedding and nonimmersion results for the manifolds$F(1,2,n)$.