arXiv subjects

Reinhold Hübl

Publications and source records attributed to Reinhold Hübl.

4 recordsLinked to original sources

arXiv2026

Equivalence of Curve Singularities and delta-Invariants

We prove that if two parameterizations of a complete reduced noetherian curve over an algebraically closed field agree modulo a sufficiently large power of the maximal ideal, then the two parameterizations are equivalent. This strengthens some bounds from Greuel and Pfister. In addition, we prove that if two reduced and irreducible curve singularities are isomorphic modulo sufficiently high (and identical) powers of their respective maximal ideals, then the completions of the two curves are isomorphic, and the isomorphism of the full completions agrees with the original isomorphism modulo some lower power of the maximal ideals. We provide a new and better bound on the lower power, strengthening the bound in Hironaka

math.AG↗

arXiv2026

Numerical Semigroups with $a_e = 2g+1$

This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be $2g+1$, where $g$ is the genus of the semigroup. We will show that these semigroups are closely related to symmetric semigroups and have interesting symmetry properties themselves. Furthermore we will show that Wilf's question has a positive answer for these semigroups and some semigroups derived thereof.

math.GR↗

arXiv2025

Optimal Parametrizations and Valuations

This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local algebra over an algebraically closed field, when treated as a subring of its integral closure. Our observations are a generalization of the more well-studied case of a numerical semigroup ring. These results provide completion to some missing arguments in certain proofs present in the existing literature, including some results concerning a long-standing conjecture of R. Berger.

math.AC↗

arXiv2014

A result on Macaulay's curve

We are able to improve what is known about two assumed homogeneous polynomials cutting out Macaulay's curve $C_4\subseteq P^3_k$ set-theoretically, in characteristic zero. We use local cohomology and an idea from Thoma.

math.AC↗