Abstract
In this chapter, we introduce Grassmannian varieties and their Schubert subvarieties; we have also included a brief introduction to flag varieties. We present the Standard Monomial Theory (abbreviated SMT) for Grassmannian and Schubert varieties. As a prime application of SMT, we present a proof of the vanishing of the higher cohomology groups of ample line bundles on the Grassmannian (and their restrictions to Schubert varieties).
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Lakshmibai, V., Brown, J. (2015). The Grassmannian and Its Schubert Varieties. In: The Grassmannian Variety. Developments in Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3082-1_5
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DOI: https://doi.org/10.1007/978-1-4939-3082-1_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3081-4
Online ISBN: 978-1-4939-3082-1
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