Bounding the degrees of generators of a homogeneous dimension 2 toric ideal
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
Let I be the toric ideal defined by a 2 x n matrix of integers, A = ((1 1 ... 1)(a_1 a_2 ... a_n)) with a_1<a_2<...<a_n. We give a combinatorial proof that I is generated by elements of degree at most the sum of the two largest differences a_i - a_(i-1). The novelty is in the method of proof: the result has already been shown by L'vovsky using cohomological arguments.
Cite
@article{arxiv.math/0204254,
title = {Bounding the degrees of generators of a homogeneous dimension 2 toric ideal},
author = {Hugh Thomas},
journal= {arXiv preprint arXiv:math/0204254},
year = {2007}
}
Comments
8 pages. To appear in Collectanea Mathematica