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Generic Cohen-Macaulay Monomial Ideals
Abdul Salam Jarrah1 and Reinhard Laubenbacher2
1Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA
jarrah@mail.etsu.edu
2Virginia Bioinformatics Institute, 1880 Pratt Drive, Blacksburg, VA 24061, USA
reinhard@vbi.vt.edu
Annals of Combinatorics 8 (1) p.45-61 March, 2004
AMS Subject Classification: 13P10, 13C14, 52B20, 52B40, 52B22
Abstract:
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree complexes.
Keywords: monomial ideals, simplicial complexes, Cohen-Macaulay

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