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TitleBetti numbers of transversal monomial ideals.
Author(s) Rahim Zaare-Nahandi
TypeArticle in Journal
AbstractIn this paper, by a modification of a previously constructed minimal free resolution for a transversal monomial ideal, the Betti numbers of this ideal is explicitly computed. For convenient characteristics of the ground field, up to a change of coordinates, the ideal of t-minors of a generic pluri-circulant matrix is a transversal monomial ideal. Using a Gröbner basis for this ideal, it is shown that the initial ideal of a generic pluri-circulant matrix is a stable monomial ideal when the matrix has two square blocks. By means of the Eliahou-Kervaire resolution for stable monomial ideals, the Betti numbers of this initial ideal is computed and it is proved that for some significant values of t, this ideal has the same Betti numbers as the corresponding transversal monomial ideal. The ideals treated in this paper naturally arise in the study of generic singularities of algebraic varieties.
Keywords Betti numbers; pluri-circulant matrix; stable monomial ideal; transversal monomial ideal
ISSN1005-3867; 0219-1733/e
URL http://www.worldscientific.com/doi/abs/10.1142/S1005386711000800
JournalAlgebra Colloq.
PublisherWorld Scientific, Singapore; Chinese Academy of Sciences, Academy of Mathematics & Systems Science,
Translation No
Refereed No