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V Lakshmibai
Articles written in Proceedings – Mathematical Sciences
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Volume 87 Issue 2 February 1978 pp 1-54
Geometry of G/P-II [The work of De Concini and Procesi and the basic conjectures]
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Volume 88 Issue 4 September 1979 pp 279-362
Geometry of
G/P —IV (Standard monomial theory for classical types) -
Volume 91 Issue 1 January 1982 pp 65-71
On the normality of the rings of Schubert varieties
We prove that the cone over a Schubert variety in
G/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. -
Volume 116 Issue 1 February 2006 pp 9-36
Standard monomial bases and geometric consequences for certain rings of invariants
Consider the diagonal action of
SL n (K) on the affine spaceX = V⊕m ⊕ (V* )⊕q whereV = K n ,K an algebraically closed field of arbitrary characteristic andm,q >n . We construct a ‘standard monomial’’ basis for the ring of invariantsK [X ]SL n (K ). As a consequence, we deduce thatK [X ]SL n (K ) is Cohen-Macaulay. We also present the first and second fundamental theorems forSL n (K)- actions . -
Volume 119 Issue 5 November 2009 pp 571-592
Wahl's Conjecture for a Minuscule $G/P$
We show that Wahl’s conjecture holds in all characteristics for a minuscule $G/P$.
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Proceedings – Mathematical Sciences
Volume 133, 2023
All articles
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