Our main theorem shows that the regularity of nondegenerate homogeneous prime ideals is
not bounded by any polynomial function of the degree; this holds over any field $ k $. In …

For X a metric space and r> 0 a scale parameter, the Vietoris–Rips simplicial complex
VR<(X; r)(resp. VR≤(X; r)) has X as its vertex set, and a finite subset σ⊆ X as a simplex …

McCullough and Peeva found counterexamples to the Eisenbud-Goto conjecture on the
Castelnuovo-Mumford regularity by using Rees-like algebras. In this paper, we suggest …

Hilbert famously showed that polynomials in $ n $ variables are not too complicated, in
various senses. For example, the Hilbert Syzygy Theorem shows that the process of …

Strength and Hartshorne’s Conjecture in high degree | Mathematische Zeitschrift Skip to main
content SpringerLink Account Menu Find a journal Publish with us Track your research Search …

Regularity of the edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs: Heliyon Skip
to Main Content Skip to Main Menu Advertisement Heliyon All content is freely available to …

The Regularity Conjecture for prime ideals in polynomial rings Page 1 EMS Surv. Math. Sci. 7
(2020), 173–206 DOI 10.4171/EMSS/38 EMS Surveys in Mathematical Sciences © European …

arXiv:2202.07696v1 [math.AC] 15 Feb 2022 Page 1 arXiv:2202.07696v1 [math.AC] 15 Feb
2022 REGULARITY OF PRIMES ASSOCIATED WITH POLYNOMIAL PARAMETRISATIONS …

Let $(R,\mathfrak {m}) $ be a complete local ring, and $ G={\rm gr} _ {\mathfrak {m}}(R) $ be
its associated graded ring. We introduce a homogenization technique which allows to relate …

In this article we obtain uniform effective upper bounds for the projective dimension and the
Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded …