Tetrahedral curves via graphs and Alexander duality
arXiv:math/0605588
Abstract
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.
15 pages; minor revisions to v. 1 to improve clarity; to appear in JPAA