Normaliz: Algorithms for Affine Monoids and Rational Cones (2009)
Bruns, Winfried, Ichim, Bogdan
Normaliz is a program for solving linear systems of inequalities. In this paper we present the algorithms implemented in the program, starting with version 2.0.
Stanley decompositions and Hilbert depth in the Koszul complex (2009)
Bruns, Winfried, Krattenthaler, Christian, Uliczka, Jan
Stanley decompositions of multigraded modules $M$ over polynomials rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition,...
A Macaulay 2 interface for Normaliz (2009)
Normaliz is a tool for the computation of Hilbert bases of normal affine monoids and related tasks. We describe the Macaulay 2 interface to Normaliz. It makes Normaliz accessible for operations on...
Koszul homology and syzygies of Veronese subalgebras (2009)
Bruns, Winfried, Conca, Aldo, Roemer, Tim
A graded K-algebra R has property N_p if it is generated in degree 1, has relations in degree 2 and the syzygies of order less or equal to p on the relations are linear. The Green-Lazarsfeld index of...
Gr\"obner bases and Betti numbers of monoidal complexes (2007)
Bruns, Winfried, Koch, Robert, Roemer, Tim
In this note we consider monoidal complexes and their associated algebras, called toric face rings. These rings generalize Stanley-Reisner rings and affine monoid algebras. We compute initial ideals...
The variety of exterior powers of linear maps (2007)
Let $K$ be a field and $V$ and $W$ be $K$-vector spaces of dimension $m$ and $n$. Let $\phi$ be the canonical map from $Hom(V,W)$ to $Hom(\wedge^t V,\wedge^t W)$. We investigate the Zariski closure...
To our children and grandchildren (2007)
Winfried Bruns, Joseph Gubeladze
Part I Cones, monoids, and triangulations 1 Polytopes, cones, and complexes................................... 3 1.A Polyhedra and their faces..................................... 3 1.B Finite...
On the integral Caratheodory property (2006)
In this note we document the existence of a finitely generated rational cone that is not covered by its unimodular Hilbert subcones, but satisfies the integral Caratheodory property. We explain the...
On the Coefficients of Hilbert Quasipolynomials (2005)
Bruns, Winfried, Ichim, Bogdan
The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert--Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients...
h-vectors of Gorenstein polytopes (2005)
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 result generalizes a...
On seminormal monoid rings (2005)
Bruns, Winfried, Li, Ping, Roemer, Tim
Given a seminormal affine monoid M we consider several monoid properties of M and their connections to ring properties of the associated affine monoid ring K[M] over a field K. We characterize when...
Cohomology of partially ordered sets and local cohomology of section rings (2005)
Brun, Morten, Bruns, Winfried, Roemer, Tim
We study local cohomology of rings of global sections of sheafs on the Alexandrov space of a partially ordered set. We give a criterion for a splitting of the local cohomology groups into summands...
Conic divisor classes over a normal monoid algebra (2004)
Let R=K[M] be a normal affine monoid algbera over a field K.Up to isomorphism the conic ideals are exactly the direct summands ofthe extension R^{1/n} of R. We show that the classes of the conic...
Bruns, Winfried, Gubeladze, Joseph
This is an overview of results from our experiment of merging two seemingly unrelated disciplines - higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the...
Groebner bases, initial ideals and initial algebras (2003)
We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.
Initial algebras of determinantal rings, Cohen-Macaulay and Ulrich ideals (2003)
Bruns, Winfried, Roemer, Tim, Wiebe, Attila
We study initial algebras of determinantal rings, defined by minors of generic matrices, with respect to their classical generic point. This approach leads to very short proofs for the structural...
Canonical modules of Rees algebras (2002)
Bruns, Winfried, Restuccia, Gaetana
We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with...
Minors of symmetric and exterior powers (2001)
Bruns, Winfried, Vasconcelos, Wolmer V.
We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski's theory of complete ideals and of...
Unimodular covers of multiples of polytopes (2001)
Bruns, Winfried, Gubeladze, Joseph
Let P be a d-dimensional lattice polytope. We show that there exists a natural number c_d, only depending on d, such that the multiples cP have a unimodular cover for every natural number c >= c_d....
Higher polyhedral K-groups (2001)
Bruns, Winfried, Gubeladze, Joseph
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's + construction are...
Bruns, Winfried, Gubeladze, Joseph
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg...
Problems and algorithms for affine semigroups (2001)
Bruns, Winfried, Gubeladze, Joseph, Trung, Ngo Viet
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems...
Let $X$ be an $n\times m$ matrix of indeterminates over a field $K$ (of sufficiently large characteristic) and $M_t$ the set of $m$-minors of $X$. We consider two objects: (1) the Ress algebra of the...
Polyhedral Algebras, Arrangements Of Toric Varieties, And Their Groups (2001)
Winfried Bruns, Joseph Gubeladze
. We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric...
Documenta Math. 463 Unimodular Covers of Multiples of Polytopes (2001)
Winfried Bruns, Joseph Gubeladze, Communicated Günter, M. Ziegler, Winfried Bruns, Joseph Gubeladze
Abstract. Let P be a d-dimensional lattice polytope. We show that there exists a natural number cd, only depending on d, such that the multiples cP have a unimodular cover for every natural number c...
The Koszul complex in projective dimension one (2000)
Let $R$ be a noetherian ring and $M$ a finite $R$-module. With a linear form $\chi$ on $M$ one associates the Koszul complex $K(\chi)$. If $M$ is a free module, then the homology of $K(\chi)$ is...
KRS and determinantal ideals (2000)
The first sections contain a survey of the application of the Knuth-Robinson-Schensted corerspondence to the computation of Groebner bases of determinantal ideals. We also set up a conceptual...
Polytopal linear algebra (2000)
Bruns, Winfried, Gubeladze, Joseph
We investigate similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory. In Section 2 we introduce the notion of a polytopal...
Polytopal linear retractions (1999)
Bruns, Winfried, Gubeladze, Joseph
We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show...
Winfried Bruns Joseph Gubeladze Martin Henk Alexander Martin Robert Weismantel (1999)
Ma Nt El, Winfried Bruns, Joseph Gubeladze, Martin Henk, Alexander Martin, Robert Weismantel
For n 6 we provide a counterexample to the conjecture that every integral vector of a n-dimensional integral polyhedral pointed cone C can be written as a nonnegative integral combination of at most...
KRS and powers of determinantal ideals (1998)
Abstract. The goal of this paper is to determine Grobner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and...
A counterexample to an integer analogue of Carathéodory's theorem (1998)
Winfried Bruns, Joseph Gubeladze, Martin Henk, Alexander Martin, Robert Weismantel
For n>5 we provide a counterexample to the conjecture that every integral vector of a n-dimensional integral polyhedral pointed cone C can be written as a nonnegative integral combination of at...
Beispiele reflexiver differentialmoduln / (1972)
Thesis (doctoral)--Technische Universität Clausthal, 1972.