Tetrahedral curves via graphs and Alexander duality

Details Tetrahedral curves via graphs and Alexander duality Tetrahedral curves via graphs and Alexander duality

2006-05-22

arxiv.org/abs/math/0605588v2

Mathematics

Commutative Algebra

15 pages; minor revisions to v. 1 to improve clarity; to appear in JPAA

Scientific paper

A tetrahedral curve is a (usually nonreduced) curve in P^3 defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph to each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen-Macaulay property.

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