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We construct a class of projective rational varieties X of any dimension m ≥ 1, which are smooth except at a point O, with the projective space ℙ m as normalization, having smooth branches, and reduced projectivized tangent cone in O. The Hilbert function of X is considered and is explicitly computed when the point O is seminormal. Indeed, we study seminormality, obtaining necessary and sufficient conditions for O to be seminormal and show that in such case the tangent cone is reduced and seminormal. [ABSTRACT FROM PUBLISHER]

Using the categorical equivalence of the class of generalized MV-algebras with the class of unital ℓ-groups, we describe all varieties of symmetric top abelian unital ℓ-groups that cover the variety Auℓ of abelian unital ℓ-groups. Equivalently, we describe all cover varieties of the variety of MV-algebras, MV, within the variety of generalized MV-algebras admitting only one negation and each of whose maximal ideals is normal. In particular, there are continuum many representable varieties of generalized MV-algebras that cover MV. [ABSTRACT FROM AUTHOR]

We prove that a finite-dimensional algebra over an algebraically closed field is of derived dimension 0 if and only if it is an iterated tilted algebra of Dynkin type. [ABSTRACT FROM AUTHOR]

For a prime p, we denote by Bn the cyclic group of order pn. Let φ be a faithful irreducible character of Bn, where p is an odd prime. We study the p-group G containing Bn such that the induced character φG is also irreducible. The purpose of this article is to determine the subgroup NG(NG(Bn)) of G under the hypothesis [NG(Bn):Bn]4 ≦ pn. [ABSTRACT FROM AUTHOR]

We give a presentation for the Chow ring of the moduli space of degree 2 stable maps from 2-pointed rational curves to the projective line. Also, integrals of all degree 4 monomials in the hyperplane pullbacks and boundary divisors of this ring are computed using equivariant intersection theory. Finally, the presentation is used to give a new computation of the (previously known) values of the genus zero, degree 2, 2-pointed gravitational correlators of the projective line. [ABSTRACT FROM AUTHOR]

As an outgrowth of the study of algebraic geometry over groups, discriminating groups were introduced. Many important universal type groups such as Higman's universal group and Thompson's group F were shown to be discriminating. Squarelike groups were then introduced to better capture axiomatic properties of discrimination. In the present article squarelike groups are reinterpreted in terms of discrimination of quasi varieties, and the relationship with an older version of discrimination, termed varietal discrimination here, is studied. [ABSTRACT FROM AUTHOR]

We consider a Birman, Ko, and Lee (BKL) presentation (defined by Vershinin, 2003) for the semigroup of singular braids SB n . We prove the embedding property for the monoid of positive singular braids and give a solution to the word and conjugacy problems in BKL generators. [ABSTRACT FROM AUTHOR]