L. Robbiano

activity

19922026

most citedSmall Groebner Fans of Ideals of Points

5 citations · 9 across the 16 of their papers we have counts for

collaborators

25 papers

math.AC2026

Border Bases and Border Basis Schemes

Lorenzo Robbiano

This survey invites the readers on a journey spanning more than twenty years of research through the landscape of border basis schemes. During most of this period, I had the pleasu…

math.AC2026

Graded Algebras over Polynomial Rings

Martin Kreuzer, Lorenzo Robbiano

Given a trivially graded polynomial ring $A = K [a_{1}, \dots, a_{m}]$ over a field $K$ and a positively graded polynomial ring $P = A [x_{1}, \dots, x_{k}]$ , we study graded rings $R = P / I$ , where $I…

math.AG2025

Re-Embeddings of Special Border Basis Schemes

Martin Kreuzer, Lorenzo Robbiano

Border basis schemes are open subschemes of the Hilbert scheme of $μ$ points in an affine space $A^{n}$ . They have easily describable systems of generators of their vanishin…

math.AC2024

Elimination by Substitution

Martin Kreuzer, Lorenzo Robbiano

Let $K$ be a field and $P = K [x_{1}, \dots, x_{n}]$ . The technique of elimination by substitution is based on discovering a coherently $Z = (z_{1}, \dots, z_{s})$ -separating tuple of polynomials $…

math.AC2023

Re-embeddings of Affine Algebras Via Gröbner Fans of Linear Ideals

Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano

Given an affine algebra $R = K [x_{1}, \dots, x_{n}] / I$ over a field $K$ , where $I$ is an ideal in the polynomial ring $P = K [x_{1}, \dots, x_{n}]$ , we examine the task of effectively calculating r…

math.AG2022

Optimal Re-Embeddings of Border Basis Schemes

Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano

Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of $P^{n}$ of given length. They yield open coverings and are easy to desc…