Bipolynomial Hilbert functions
Algebraic Geometry
2009-10-20 v1 Commutative Algebra
Abstract
Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively, the Hilbert function and the Hilbert polynomial of X. We say that X has bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every non-negative integer d. We show that if X consists of a plane and generic lines, then X has bipolynomial Hilbert function. We also conjecture that generic configurations of non-intersecting linear spaces have bipolynomial Hilbert function.
Cite
@article{arxiv.0910.3569,
title = {Bipolynomial Hilbert functions},
author = {E. Carlini and M. V. Catalisano and A. V. Geramita},
journal= {arXiv preprint arXiv:0910.3569},
year = {2009}
}