Abstract
In this chapter, using standard monomial basis, we prove Cohen–Macaulayness and normality for Schubert varieties; these geometric properties are proved even for the cones over Schubert varieties. We also give a characterization of arithmetically factorial Schubert varieties. The chapter also includes determination of the singular locus of a Schubert variety, and the tangent space at a singular point of a Schubert variety.
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Lakshmibai, V., Brown, J. (2015). Further Geometric Properties of 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_6
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DOI: https://doi.org/10.1007/978-1-4939-3082-1_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3081-4
Online ISBN: 978-1-4939-3082-1
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