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

2002/04/22 by Hugh Thomas, Thomas, Hugh
Mathematics · #05A17 (Secondary) #13F20 (Primary) 14M25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:05A17 #msc:13F20 #msc:14M25

paper · pdf · doi:10.48550/arxiv.math/0204254

8 pages. To appear in Collectanea Mathematica

arxiv created 2002/04/22 · arxiv updated 2009/11/30

Abstract

Let I be the toric ideal defined by a 2 x n matrix of integers, A = ((1 1 ... 1)(a₁ a₂ ... a_n)) with a₁<a₂<...<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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