Subspace arrangements defined by products of linear forms (2004)
Björner, Anders, Peeva, Irena, Sidman, Jessica
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial...
We introduce and study the toric Hilbert scheme that parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal.
Resolutions and lattices (2002)
We discuss how lattices and posets can be used as tools to study minimal free resolutions of monomial or toric ideals.
Finite regularity and Koszul algebras (2001)
Avramov, L. L. (Luchezar L.), 1948-, Peeva, Irena.
American Journal of Mathematics - Volume 123, Number 2, April 2001
TORIC HILBERT SCHEMES Irena Peeva Mike Stillman (2001)
: We introduce and study the toric Hilbert scheme which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. 1. Introduction The classical Hilbert scheme,...
: We introduce and study the toric Hilbert scheme which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. 1. Introduction The classical Hilbert scheme,...
Finite Regularity And Koszul Algebras (2000)
Luchezar L. Avramov, Irena Peeva
. We determine the positively graded commutative algebras over which the residue eld modulo the homogeneous maximal ideal has nite Castelnuovo-Mumford regularity: they are the polynomial rings in...
Boundedness Versus Periodicity Over Commutative Local Rings (2000)
Vesselin Gasharov, Irena Peeva
: Over commutative graded local artinian rings, examples are constructed of periodic modules of arbitrary minimal period and modules with constant Betti numbers which are not eventually periodic....
Finite Regularity And Koszul Algebras (2000)
Luchezar L. Avramov, Irena Peeva
: We determine the positively graded commutative algebras over which the residue field modulo the homogeneous maximal ideal has finite Castelnuovo-Mumford regularity: they are the polynomial rings in...
The LCM-Lattice in Monomial Resolutions (1999)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
this paper we obtain results on the minimal free resolution of an arbitrary monomial ideal. We introduce a new approach inspired by the topological theory of subspace arrangements. Some of the best...
THE LCM-LATTICE in MONOMIAL RESOLUTIONS (1999)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
Introduction Describing the properties of the minimal free resolution of a monomial ideal I is a difficult problem posed in the early 1960's. The main directions of progress on this problem were: ffl...
Hyperplane Arrangements And Linear Strands In Resolutions (1999)
this paper A stands for a central hyperplane arrangement of hyperplanes H 1 ; : : : ; H n
this paper A stands for a central hyperplane arrangement of hyperplanes H 1 ; : : : ; H n
Deformations Of Codimension 2 Toric Varieties (1998)
Vesselin Gasharov, Irena Peeva
: We prove Sturmfels' conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Grobner basis theory. 1. Introduction The properties of ideals with a...
Rationality For Generic Toric Rings (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We study generic toric rings. We prove that they are Golod rings, so the Poincar'e series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also...
Coordinate Subspace Arrangements and Monomial Ideals (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We relate the (co)homological properties of real coordinate subspace arrangements and of monomial ideals. 1. Introduction In [PRW] we describe the cohomological properties of a real diagonal...
RATIONALITY FOR GENERIC TORIC RINGS Vesselin Gasharov Irena Peeva Volkmar Welker (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We study generic toric rings. We prove that they are Golod rings, so the Poincar'e series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also...
DEFORMATIONS OF CODIMENSION 2 TORIC VARIETIES Vesselin Gasharov Irena Peeva (1998)
Vesselin Gasharov, Irena Peeva
: We prove Sturmfels' conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Grobner basis theory. 1. Introduction The properties of ideals with a...
Irena Peeva, Victor Reiner, Bernd Sturmfels
. For a finitely generated submonoid of N d , we consider the minimal free resolution of a field k as a module over the monoid algebra k[]. Interpreting the ranks of the free modules in the...
Non-Commutative Gr Obner Bases For Commutative Algebras (1998)
David Eisenbud, Irena Peeva, Bernd Sturmfels
this paper. Typeset by A M S-T E X 2 DAVID EISENBUD, IRENA PEEVA AND BERND STURMFELS
Cohomology Of Real Diagonal Subspace Arrangements Via Resolutions (1998)
Irena Peeva, Vic Reiner, Volkmar Welker
: We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the...
GENERIC LATTICE IDEALS Irena Peeva Bernd Sturmfels (1998)
this paper are:
Dave Bayer, Irena Peeva, Bernd Sturmfels
this paper is that there exists a genericity condition, which ensures simply structured homological behavior. The same idea is developed further for toric varieties in [PS]. We call a monomial ideal...
Syzygies Of Codimension 2 Lattice Ideals (1998)
this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x 1 ; : : : ; x n ] over a field k and identify monomials x
GENERIC LATTICE IDEALS Irena Peeva Bernd Sturmfels (1998)
this paper are:
Dave Bayer, Irena Peeva, Bernd Sturmfels
this paper is that there exists a genericity condition, which ensures simply structured homological behavior. The same idea is developed further for toric varieties in [PS]. We call a monomial ideal...
Cohomology Of Real Diagonal Subspace Arrangements Via Resolutions (1997)
Irena Peeva, Vic Reiner, Volkmar Welker
We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the...
GENERIC LATTICE IDEALS Irena Peeva Bernd Sturmfels (1997)
this paper are:
Irena Peeva, Victor Reiner, Bernd Sturmfels
For a finitely generated submonoid Λ of N^d, we consider minimal free resolutions of a field k as a module over the monoid algebra k[Λ]. Using a result of Laudal and Sletsjøe...
Bayer, Dave, Peeva, Irena, Sturmfels, Bernd
Call a monomial ideal M "generic" if no variable appears with the same nonzero exponent in two distinct monomial generators. Using a convex polytope first studied by Scarf, we obtain a minimal free...
Dave Bayer, Irena Peeva, Bernd Sturmfels
this paper we prove that the minimal free resolution for any generic monomial ideal M
Dave Bayer, Irena Peeva, Bernd Sturmfels
this paper we prove that the minimal free resolution for any generic monomial ideal M comes from a simplicial complex Delta M , which we call the Scarf complex of M .
Non-Commutative Gröbner Bases For Commutative Algebras (1996)
David Eisenbud, Irena Peeva, Bernd Sturmfels
this paper. Typeset by A M S-T E X 2 DAVID EISENBUD, IRENA PEEVA AND BERND STURMFELS
Non-Commutative Gr Obner Bases For Commutative Algebras (1996)
David Eisenbud, Irena Peeva, Bernd Sturmfels
this paper. Typeset by A M S-T E X 1
Irena Peeva, Victor Reiner, Bernd Sturmfels
We study monoid algebras which possess an initial ideal that is the Stanley-Reisner ideal of a poset. We construct a quadratic non-commutative Grobner basis which induces non-pure shellings for all...