Unmixed Graphs that are Domains

Details Unmixed Graphs that are Domains Unmixed Graphs that are Domains

2009-01-25

arxiv.org/abs/0901.3897v3

Comm. Alg. vol. 39 n. 7 (2011), pp. 2260-2267

Mathematics

Commutative Algebra

Revised version, 8 pages

Scientific paper

Given an arbitrary graph G, we study its basic covers algebra, which is the symbolic fiber cone of the Alexander dual of the edge ideal of G. Extending results of Villarreal and Benedetti-Constantinescu-Varbaro, valid only in the case when G is bipartite, we characterize in a combinatorial fashion the situations when: 1) the basic covers algebra is a domain, and 2) it is a domain and in addition (the edge ideal of) G is unmixed. It turns out that the last result gives a complete characterization of those graphs for which any symbolic power of the edge ideal is generated by monomials of the same degree.

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