w-Divisorial domains

Divisorial rings and Cox rings

1 Preliminaries on monoids Definition 1.1. An Abelian monoid is a set with a binary, associative, and commutative operation which has a neutral element. It will often be called just a monoid in this manuscript because we will not deal with non-commutative monoids. A monoid M is called • finitely generated if there is a finite set of generators, or equivalently if there is a surjection of monoid...

Quotients of Divisorial Toric

Nanoridge domains in a-phase W films

Two types of nanoridge domains oriented with each other with an angle ranging between 109 and 124 were measured by scanning tunneling microscopy on the a-W film sputter deposited on an oxidized Si surface. Each domain contains nanoridges with a period of 7.5 1.0 nm. No such domains were observed on the b-W film surface. We argued that due to the anisotropy of the W(1 1 0) surface, the impinging...

Quotients of Divisorial Toric Varieties

We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a categorical quotient in the category of divisorial varieties. Our result generalizes previous statements for the quasiprojective case. A first step in the proo...

Divisorial Linear Algebra of Normal Semigroup Rings

We investigate the minimal number of generators μ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely divisorial ideals I such that μ(I) ≤ C. It follows that there...