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On the normality of the rings of Schubert varieties

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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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Authors and Affiliations

  1. Department of Mathematics, The University of Michigan, 48109, Ann Arbor, Michigan, USA

    C. Huneke & V. Lakshmibai

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  1. C. Huneke
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  2. V. Lakshmibai
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Huneke, C., Lakshmibai, V. On the normality of the rings of Schubert varieties. Proc. Indian Acad. Sci. (Math. Sci.) 91, 65–71 (1982). https://doi.org/10.1007/BF02837262

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