The class of all M -solid varieties of a given type τ forms a complete sublattice of the lattice L(τ) of all varieties of algebras of type τ . This gives a tool for a better description of the lattice L(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon char...

Hilbert-Siegel varieties are moduli spaces for abelian varieties equipped with an action by an order OK in a fixed, totally real field K. As such, they include both the Siegel moduli spaces (use K = Q and the action is the standard one) and Hilbert-Blumenthal varieties (where the dimension of K is the same as that of the abelian varieties in question). In this paper we study certain phenomena a...

Thirty-nine commercial varieties of head cabbage were evaluated for feeding preference of the diamondback moth (DBM), Plutella xylostella, at Kula, Hawaii, USA. Varieties were evaluated for density of caterpillars, extent of feeding damage and percentage of marketable heads. Twelve out of 39 (31%) varieties that showed the least DBM caterpillar damage and produced high percentage of marketable ...

This list of the North American vegetable cultivars was developed using the database of cultivars registered with the American Seed Trade Association, as well as published descriptions from scientific journals, seed catalogs, and websites of seed companies. Assistant editors responsible for each crop were instructed to obtain as much information as possible about the cultivars available to Nort...

We describe the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In particular, we generalize the results on MMP in toric varieties due to M. Reid, and we complete the results on MMP in spherical varieties due to M. Brion in the case of hor...

This paper is a general survey of work on Goppa-type codes from higher dimensional algebraic varieties. The construction and several techniques for estimating the minimum distance are described first. Codes from various classes of varieties, including Hermitian hypersurfaces, Grassmannians, flag varieties, ruled surfaces over curves, and Deligne-Lusztig varieties are considered. Connections wit...

Let IM and IN be defining ideals of toric varieties such that IM is a projection of IN , i.e. IN ⊆ IM . We give necessary and sufficient conditions for the equality IM = rad(IN + (f1, . . . , fs)), where f1, . . . , fs belong to IM . Also a method for finding toric varieties which are set-theoretic complete intersection is given. Finally we apply our method in the computation of the arithmetica...

In this paper we deal with two foundational questions on complete differential algebraic varieties. We establish, by means of the differential algebraic version of Bertini’s theorem and assuming a weaker form of the catenary conjecture, that in order to verify (differential) completeness one can restrict second factors to zero-dimensional differential varieties. Then, we extend Kolchin’s result...

We construct Nakajima’s quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy’s) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima’s quiver varieties and a decomposition of an affine Grassmannian i...