Related papers: w-Divisorial Domains
An integral domain $D,$ with quotient field $K,$ is a $v$-domain if for each nonzero finitely generated ideal $A$ of $D$ we have $(AA^{-1})^{-1}=D.$ It is well known that if $D$ is a $v$-domain$,$ then some quotient ring $D_{S}$ of $D$ may…
Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor. We study a natural linear system in $|K_X + L|$.…
Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, narrow wires N\'eel walls. Here, the transition region is investigated by direct imaging of the wall…
While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We…
This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we show that every divisorial valuation over an algebraic variety corresponds to an irreducible closed subset of the arc space. Then we define the…
Gr\"obner bases are a fundamental tool when studying ideals in multivariate polynomial rings. More recently there has been a growing interest in transferring techniques from the field case to other coefficient rings, most notably Euclidean…
We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.
An integral domain $D$ is a {\em valuation ideal factorization domain} (VIFD) if each nonzero principal ideal of $D$ can be written as a finite product of valuation ideals. Clearly, $\pi$-domains are VIFDs. We study the ring-theoretic…
We give sufficient conditions on planar domains for polynomials to be dense in the algebras A and A-infinity of the product of these domains, endowed with their natural topologies. We also characterize the uniform limits, with respect to…
For a given family $(G_i)_{i \in \N}$ of finitely generated abelian groups, we construct a Dedekind domain $D$ having the following properties. \begin{enumerate} \item $\Pic(D) \cong \bigoplus_{i \in \N}G_i$. \item For each $i \in \N$,…
The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by t-multiplication. This paper investigates integral domains with Boolean t-class semigroup with an emphasis…
We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial.
Domain generalization approaches aim to learn a domain invariant prediction model for unknown target domains from multiple training source domains with different distributions. Significant efforts have recently been committed to broad…
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…
Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is itself a Calabi-Yau. Corollary: A smooth…
In this paper we study the class of $w$-Jaffard domains in pullback constructions, and give new examples of these domains. In particular we give examples to show that the two classes of $w$-Jaffard and Jaffard domains are incomparable. As…
We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. We provide upper and lower bounds on the dimensions of Voronoi cells. For algebraic varieties, we count their full-dimensional Voronoi cells. As an…
This paper studies the class group of graded integral domains. As an application, we state a decomposition theorem for class groups of semigroup rings. This recovers well-known results developed for the classic contexts of polynomial rings…
In this paper, we consider five possible extensions of the Pr\"ufer domain notion to the case of commutative rings with zero-divisors. We investigate the transfer of these Pr\"ufer-like properties between a ring $R$ and $R\bowtie I$; his…
We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…