Complete intersections in toric ideals

Cattani, Eduardo; Curran, Raymond; Dickenstein, Alicia

doi:10.1090/S0002-9939-06-08513-3

Complete intersections in toric ideals
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by Eduardo Cattani, Raymond Curran and Alicia Dickenstein PDF

Proc. Amer. Math. Soc. 135 (2007), 329-335 Request permission

Abstract:

We present examples that show that in dimension higher than one or codimension higher than two, there exist toric ideals $I_A$ such that no binomial ideal contained in $I_A$ and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.

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