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In this thesis, we have shown that Plucker relations of the Grassmannvariety Grd,n is a Grobner basis for its homogenous ideal relative to the graded reverse lexicographic order and the ssociated basis of the homogenous coordinate ring is the well-known standard monomial basis. Moreover, we carry this construction over the Schubert subvarieties of Grd,n. Keywords: Grobner Bases, Standard Monomials, Grassmannians |