A geometric approach to Standard Monomial Theory
By M. Brion, V. Lakshmibai. 2001
68 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/93e0998412227416cb68a716776357c11900b14b
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Singularities of Generalized Richardson Varieties (2010, methodology): “We refer the reader to [ 6-9 ] for more information about higher cohomology of line bundles on Richardson varieties.”
- Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “ 0 for all α∈ Ew. Proof. Assertion (1) is an elementary computation, which is left to the reader. Assertion (2) follows immediately using Lemma 4.1.1. Part (3) is Chevalley’s formula, see for example [BL03] §1, page 654. Note that we are using a slightly different parametrization than in loc. cit.. T”