In this paper, for any simple, simply connected algebraic group G of type B, C or D and for any maximal parabolic subgroup P of G, we describe all minimal dimensional Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P . We also describe, for any semi-simple simply connected algebraic group G and for any Borel subgroup B of G, all Coxeter elements τ for which the Schubert variety X(τ ) admits a semistable point for the action of the torus T with respect to a non-trivial line bundle on G/B.

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Abstract. In this paper, we prove that for any finite dimensional vector space V over an algebraically closed field k, and for any finite subgroup G of GL(V ) which is either solvable or is generated by pseudo reflections such that |G| is a unit in k, the projective variety P(V )/G is projectively normal with respect to the descent of O(1) ⊗|G| .

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