Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book
covers the standard topics in toric geometry; a novel feature is that each of the first nine …

The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

A combinatorial criterion for the toric ideal arising from a finite graph to be generated by
quadratic binomials is studied. Such a criterion guarantees that every Koszul algebra …

We completely characterize sections of the cones of nonnegative polynomials, convex
polynomials and sums of squares with polynomials supported on circuits, a genuine class of …

The aim of this paper is to study alcoved polytopes, which are polytopes arising from affine
Coxeter arrangements. This class of convex polytopes includes many classical polytopes …

A graded k-algebra A is called a Ivoszul algebra if the minimal graded free A-resolution of k
has only linear maps. This article is a survey on results obtained about Ivoszul algebras …

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric
geometry, we work with modules over a polynomial ring graded by a finitely generated …

We show that the Ehrhart h-vector of an integer Gorenstein polytope with a regular
unimodular triangulation satisfies McMullen's g-theorem; in particular, it is unimodal. This …