On the normality of the rings of Schubert varieties |
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Authors: | C Huneke V Lakshmibai |
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Institution: | (1) Department of Mathematics, The University of Michigan, 48109 Ann Arbor, Michigan, USA |
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Abstract: | We prove that the cone over a Schubert variety inG/P (P being a maximal parabolic subgroup of classical type) is normal by exhibiting a 2-regular sequence inR(w) (the homogeneous coordinate ring of the Schubert varietyX(w) inG/P under the canonical protective embeddingG/P ⊂→ (p (H° G/P,L)),L being the ample generator of (PicG/P), which vanishes on the singular locus ofX(w). We also prove the surjectivity ofH° (G/Q, L) H° (X(w), L), whereQ is a classical parabolic subgroup (not necessarily maximal) ofG andL is an ample line bundle onG/Q. |
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Keywords: | Schubert varieties parabolic subgroups standard monomials normality |
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