201 citations · 429 across the 6 of their papers we have counts for
6 papers
Syzygies of Unimodular Lawrence Ideals
Dave Bayer, Sorin Popescu, Bernd Sturmfels
Infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra. The quotient of such an arrangement modulo the lattice act…
Extremal Betti Numbers and Applications to Monomial Ideals
Dave Bayer, Hara Charalambous, Sorin Popescu
In this short note we introduce a notion of extremality for Betti numbers of a minimal free resolution, which can be seen as a refinement of the notion of Mumford-Castelnuovo regul…
Cellular Resolutions of Monomial Modules
Dave Bayer, Bernd Sturmfels
We construct a canonical free resolution for arbitrary monomial modules and lattice ideals. This includes monomial ideals and defining ideals of toric varieties, and it generalizes…
Monomial Resolutions
Dave Bayer, Irena Peeva, Bernd Sturmfels
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 obta…
What can be computed in algebraic geometry?
Dave Bayer, David Mumford
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geom…
Grobner bases and extension of scalars
Dave Bayer, Andre Galligo, Mike Stillman
This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension i…