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 …

We resolve Stillman's conjecture for families of polynomial rings that are graded by any
abelian group under mild conditions. Conversely, we show that these conditions are …

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a
uniform upper bound for the projective dimension of all homogeneous ideals, in polynomial …

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 …

On the degrees and complexity of algebraic varieties Page 1 Degrees of Projective Varieties
Jason McCullough Outline Introduction Degree of a variety Regularity Gröbner bases …