We express the Segre class of a monomial scheme—or, more generally, a scheme monomially supported on a set of divisors cutting out complete intersections— in terms of an integral computed over an associated body in euclidean space. The formula is in the spirit of the classical Bernstein-Kouchnirenko theorem computing intersection numbers of equivariant divisors in a torus in terms of mixed volu...

Natural intersection type preorders are the type structures which agree with the plain intuition of intersection type constructor as set-theoretic intersection operation and arrow type constructor as set-theoretic function space constructor. In this paper we study the relation between natural intersection type preorders and natural λ-structures, i.e. ω-algebraic lattices D with Galois connectio...

Natural intersection type preorders are the type structures which agree with the plain intuition of intersection type constructor as set-theoretic intersection operation and arrow type constructor as set-theoretic function space constructor. In this paper we study the relation between natural intersection type preorders and natural λ-structures, i.e. ω-algebraic lattices D with Galois connectio...

Natural intersection type preorders are the type structures which agree with the plain intuition of intersection type constructor as set-theoretic intersection operation and arrow type constructor as set-theoretic function space constructor. In this paper we study the relation between natural intersection type preorders and natural λ-structures, i.e. ω-algebraic lattices D with Galois connectio...

We describe a class of toric varieties which are set-theoretic complete intersections only over fields of one positive characteristic p.

In this paper, we introduce the notion of “extension” of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one singl...

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...