M. Toeniskoetter

activity

20132026

most citedIdeal theory of infinite directed unions of local quadratic transforms

2 citations · 2 across the 6 of their papers we have counts for

collaborators

9 papers

math.AC2026

Interval Rings

William Heinzer, K. Alan Loper, Bruce Olberding +1

Interval rings comprise a class of one-dimensional integrally closed local integral domains which are overrings of a two-dimensional regular local ring. We construct them by inters…

math.AC2024

Connectedness and integrally closed local overrings of two-dimensional regular local rings

William Heinzer, K. Alan Loper, Bruce Olberding +1

Let $D$ be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of $D$ that dominat…

math.AC2023

A connectedness theorem for spaces of valuation rings

William Heinzer, K. Alan Loper, Bruce Olberding +1

Let $F$ be a field, let $D$ be a local subring of $F$ , and let Val $_{F} (D)$ be the space of valuation rings of $F$ that dominate $D$ . We lift Zariski's connectedness theorem for fibe…

math.AC2017

Directed unions of local quadratic transforms of regular local rings and pullbacks

Lorenzo Guerrieri, William Heinzer, Bruce Olberding +1

Let ${R_{n}, m_{n}}_{n \geq 0}$ be an infinite sequence of regular local rings with $R_{n + 1}$ birationally dominating $R_{n}$ and $m_{n} R_{n + 1}$ a principal idea…

math.AC2016

Blowing Up Finitely Supported Complete Ideals in a Regular Local Ring

William Heinzer, Youngsu Kim, Matthew Toeniskoetter

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). We consider singularities of the normalization of the blow-up Proj R[It] of I. A theorem of L…

math.AC2016

Directed Unions of Local Quadratic Transforms of a Regular Local Ring

William Heinzer, Mee-Kyoung Kim, Matthew Toeniskoetter

We consider the directed union S of an infinite sequence {(R_n, m_n)} of successive local quadratic transforms of a regular local ring (R, m). If dim R = 2, Abhyankar proves that S…

math.AC2015

Asymptotic properties of infinite directed unions of local quadratic transforms

William Heinzer, Bruce Olberding, Matthew Toeniskoetter

We consider infinite sequences {R_n} of successive local quadratic transforms of a regular local ring. Let S denote the directed union of the sequence of regular local rings R_n. W…

math.AC2015★ 2 cited

Ideal theory of infinite directed unions of local quadratic transforms

W. Heinzer, K. A. Loper, B. Olberding +2

Let $R$ be a regular local ring of dimension at least 2. Associated to each valuation domain birationally dominating $R$ , there exists a unique sequence ${R_{n}}$ of local quadrati…

math.AC2013

Finitely Supported *-Simple Complete Ideals in a Regular Local Ring

William Heinzer, Mee-Kyoung Kim, Matthew Toeniskoetter

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). A theorem of Lipman implies that I has a unique factorization as a *-product of special *-sim…