A geometric approach to Standard Monomial Theory
代数几何
2007-05-23 v1 表示论
摘要
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.
引用
@article{arxiv.math/0111054,
title = {A geometric approach to Standard Monomial Theory},
author = {M. Brion and V. Lakshmibai},
journal= {arXiv preprint arXiv:math/0111054},
year = {2007}
}
备注
AMSLaTeX, 36 pages