Toric geometry of cuts and splits

Details Toric geometry of cuts and splits Toric geometry of cuts and splits

2006-06-27

arxiv.org/abs/math/0606683v2

Mathematics

Commutative Algebra

18 pages

Scientific paper

Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial structure of the graph and the corresponding cut polytope to algebraic properties of the ideal. Cut ideals generalize toric ideals arising in phylogenetics and the study of contingency tables.

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