We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in $SL\left(n\right)/B$, Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus,...

Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension 2 in projective space. In this paper we study points in P3 and curves in P4 in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot decide the outcome. This examples are candidates for counterexamples to the hoped-for extensions of codimension...

Dans cet article, nous étudions le schéma de Hilbert $H_{d,g}$ des courbes gauches (de pure dimension 1 et sans points immergés) de degré $d\ge 4$ et genre $g=(d-3)(d-4)/2$, qui est le plus grand genre pour lequel l’étude de $H_{d,g}$ est non triviale. Nous commençons par donner, pour chaque valeur de $d$, tous les modules de Rao des courbes de $H_{d,g}$ et ses sous-schémas à cohomologie constante, et nous décrivons la courbe générique de chacun de ces sous-schémas. Nous déduisons ensuite les composantes irréductibles et la dimension de $H_{d,g}$. Enfin,...