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 …

Let I and J be nonzero ideals in two Noetherian algebras A and B over a field k. Let I+ J I+ J
denote the ideal generated by I and J in A ⊗ _k BA⊗ k B. We prove the following expansion …

We study several properties of multihomogeneous prime ideals. We show that the
multigraded generic initial ideal of a prime has very special properties, for instance, its …

The purpose of this paper is to establish a Castelnuovo-Mumford regularity bound for
threefolds with mild singularities. Let X be a non-degenerate normal projective threefold in P …

We answer several natural questions which arise from a recent paper of McCullough and
Peeva providing counterexamples to the Eisenbud–Goto Regularity Conjecture. We give …

The key object in the Ehrhart theory of lattice polytopes is the numerator polynomial of the
rational generating series of the Ehrhart polynomial, called-polynomial. In this article, we …

In this paper, to any subset A⊂ Z n we explicitly associate a unique monomial projection Y
n, d A of a Veronese variety, whose Hilbert function coincides with the cardinality of the t-fold …

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 …

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 …

Given a collection of $ t $ subspaces in an $ n $-dimensional $ mathbb {K} $-vector space $
W $, we can associated to them $ t $ vanishing ideals in the symmetric algebra $ mathcal …