Cones of Hilbert functions
Commutative Algebra
2016-05-27 v1 Algebraic Geometry
Abstract
We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generated by the Hilbert functions of all modules, all modules with bounded a-invariant, and all modules with bounded Castelnuovo-Mumford regularity. The first of these cones is infinite-dimensional and simplicial, the second is finite-dimensional but neither simplicial nor polyhedral, and the third is finite-dimensional and simplicial.
Keywords
Cite
@article{arxiv.1404.7341,
title = {Cones of Hilbert functions},
author = {Mats Boij and Gregory G. Smith},
journal= {arXiv preprint arXiv:1404.7341},
year = {2016}
}
Comments
20 pages, 2 figures