Let $ n, d,\eta $ be positive integers. We show that in a polynomial ring $ R $ in $ N $
variables over an algebraically closed field $ K $ of arbitrary characteristic, any $ K …

The purpose of this paper is to prove that certain limits of polynomial rings are themselves
polynomial rings, and show how this observation can be used to deduce some interesting …

In an earlier work, the authors prove Stillman's conjecture in all characteristics and all
degrees by showing that, independent of the algebraically closed field $ K $ or the number …

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 …

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 …

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree
three. Motivated by Stillman's question, Engheta proved that the projective dimension pd …

Let I be an ideal generated by quadrics in a standard graded polynomial ring S over a field.
A question of Avramov, Conca, and Iyengar asks whether the Betti numbers of R= S/I over S …

This report is divided into seven chapters. In chapter one, graded resolutions are introduced
and some related fundamental results are proved. In chapter two, we discuss Gröbner bases …

Let S be a polynomial ring over an algebraically closed field k and \mathfrakp=(x,y,z,w) a
homogeneous height 4 prime ideal. We give a finite characterization of the degree 2 …

Let R (h) denote the polynomial ring in variables x 1,…, xh over a specified field K. We
consider all of these rings simultaneously, and in each use lexicographic (lex) monomial …