Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.3917

Groebner bases for spaces of quadrics of codimension 3

Aldo Conca
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let $R=\oplus_{i\geq 0} R_i$ be an Artinian standard graded $K$-algebra defined by quadrics. Assume that $\dim R_2\leq 3$ and that $K$ is algebraically closed of characteristic $\neq 2$. We show that $R$ is defined by a Gröbner basis of quadrics with, essentially, one exception. The exception is given by $K[x,y,z]/I$ where $I$ is a complete intersection of 3 quadrics not containing the square of a linear form.

Explore related subjects

math.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Aldo Conca. 2008-04-02. Groebner bases for spaces of quadrics of codimension 3. https://arxiv.org/abs/0709.3917

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Cotorsion pairs and Tor-pairs over commutative noetherian rings

For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of the ring. Each such function gives rise to a system of local depth conditions which describes the left-hand class in the corresponding cotorsion pair. Furthermore, we show that these cotorsion pairs correspond by explicit duality to hereditary Tor-pairs generated by modules of finite flat dimension.

math.AC↗
arXiv2026

Boolean Rank via Monomial Ideals

Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying structure in the data. When interpreting a binary matrix as the adjacency matrix of a bipartite graph, BMF is equivalent to the NP-hard biclique cover problem. By approaching this problem through the lens of commutative algebra, we utilize algebraic structures and techniques--particularly the Castelnuovo-Mumford regularity of combinatorially defined ideals--to establish new lower bounds for Boolean matrix rank.

math.AC↗
arXiv2026

Conjugation Differential Invariants of $\mathrm{SL}_2(\mathbb{F}_q)$ on trace-free matrices

Let $q=p^k$ be prime power, let $F= \mathbb{F}_q$ and let $V$ be the vector space of 2 by 2 matrices over $F$ with trace zero. Let $G = \mathrm{SL}_2(F)$. Then $G$ acts on $V$ via conjugation. Let $Ω= S(V^*) \otimes Λ(V^*)$ be the algebra of differential forms on $V$. A minimal generating set for $Ω^G$ when $q=3$ was computed by the author and Meyer. In this article we compute a minimal generating set for $Ω^G$ for all $q$.

math.AC↗