We give examples of proper normal surfaces that are not embeddable into simplicial toric prevarieties nor toric prevarieties of affine intersection.

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hype...

We relate vertex decompositions of simplicial complexes to Gröbner degeneration, in stages, of affine varieties. v cone on the link deletion

We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the Auslander Conjecture. Along the way, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups of π1 to have vanishing...

A numerical semigroup $S$ is an additive subsemigroup of the non-negative integers with finite complement, and squarefree divisor complex element $m \in S$ a simplicial $\Delta_m$ that arises in study multigraded Betti numbers. We compute complexes for certain classes semigroups, exhibit new family are occur as some element.

In [3] Bruns, Gubeladze, and Trung define the notion of polytopal semigroup ring as follows. Let P be a lattice polytope in R, i. e. a polytope whose vertices have integral coordinates, and K a field. Then one considers the embedding ι : R → R, ι(x) = (x, 1), and chooses SP to be the semigroup generated by the lattice points in ι(P ); the K-algebra K[SP ] is called a polytopal semigroup ring. S...