Dimension, Depth and Zero-Divisors of the Algebra of Basic k-Covers of a Graph

Benedetti, Bruno and Constantinescu, Alexandru and Varbaro, Matteo. (2008) Dimension, Depth and Zero-Divisors of the Algebra of Basic k-Covers of a Graph. Matematiche, 63 (2). pp. 117-156.

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We study the basic k-covers of a bipartite graph G; the algebra A(G) they span, first studied by Herzog, is the fiber cone of the Alexander dual of the edge ideal. We characterize when A(G) is a domain in terms of the combinatorics of G; it follows from a result of Hochster that when A(G) is a domain, it is also Cohen-Macaulay. We then study the dimension of A(G) by introducing a geometric invariant of bipartite graphs, the “graphical dimension”. We show that the graphical dimension of G is not larger than dim(A(G)), and equality holds in many cases (e.g. when G is a tree, or a cycle). Finally, we discuss applications of this theory to the arithmetical rank.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Gorla)
UniBasel Contributors:Constantinescu, Alexandru
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Dipartimento di Matematica e Informatica
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:19 Dec 2017 10:56
Deposited On:19 Dec 2017 10:53

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