Combinatorics of symbolic Rees algebras of edge ideals of clutters

Details Combinatorics of symbolic Rees algebras of edge ideals of clutters Combinatorics of symbolic Rees algebras of edge ideals of clutters

2009-05-07

arxiv.org/abs/0905.0938v2

Contemp. Math. 555 (2011), 151--164

Mathematics

Commutative Algebra

Contemp. Math., to appear

Scientific paper

Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I. It is shown that the minimal generators of Rs(I) are in one to one correspondence with the irreducible parallelizations of C. From our description some major results on symbolic Rees algebras of perfect graphs and clutters will follow. As a byproduct, we give a method, using Hilbert bases, to compute all irreducible parallelizations of C along with all the corresponding vertex covering numbers.

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