A geometric approach to Standard Monomial Theory

Details A geometric approach to Standard Monomial Theory A geometric approach to Standard Monomial Theory

2001-11-06

arxiv.org/abs/math/0111054v1

Mathematics

Algebraic Geometry

AMSLaTeX, 36 pages

Scientific paper

We obtain a geometric construction of a ``standard monomial basis'' for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert varieties, opposite Schubert varieties, and unions of intersections of these varieties. Our approach relies on vanishing theorems and a degeneration of the diagonal ; it also yields a standard monomial basis for the multi-homogeneous coordinate rings of flag varieties of classical type.

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