Bounding the degrees of generators of a homogeneous dimension 2 toric ideal
Abstract
Let I be the toric ideal defined by a 2 x n matrix of integers, A = ((1 1 ... 1)(a1 a2 ... an)) with a1<a2<...<an. We give a combinatorial proof that I is generated by elements of degree at most the sum of the two largest differences ai - a(i-1). The novelty is in the method of proof: the result has already been shown by L'vovsky using cohomological arguments.
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