The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...

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...

We show how to calculate three low degree set-theoretic generators (i.e., algebraic surfaces) for all rational space curves of low degree (degree ≤ 6) as well as for all higher degree rational space curveswhere at least one element of theirμ-basis has degree 1 from a μ-basis of the parametrization. In addition to having low degree, at least two of these surface generators are always ruled surfa...

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

This paper presents a set description logic with subsorts, feature selection (the inverse of unary function application), agreement, intersection , union and complement. We deene a model theoretic open world semantics and show that sorted feature structures constitute a canon-ical model, that is, without loss of generality subsumption and consistency of set descriptions can be considered with r...

A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) Calabi-Yau complete intersection models and the corresponding chiral operators in Landau-Ginzburg orbifolds. The well known polynomial deformations are thus generalized and the universal but somewhat abstract Koszul computations acquire a concrete realization and a general but more heuristic rein...