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Bounding the degrees of generators of a homogeneous dimension 2 toric ideal

Hugh Thomas
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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.

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Hugh Thomas. 2002-04-22. Bounding the degrees of generators of a homogeneous dimension 2 toric ideal. https://arxiv.org/abs/math/0204254

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