2 research outputs found
Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs
In this paper we study irreducible representations and symbolic Rees algebras
of monomial ideals. Then we examine edge ideals associated to vertex-weighted
oriented graphs. These are digraphs having no oriented cycles of length two
with weights on the vertices. For a monomial ideal with no embedded primes we
classify the normality of its symbolic Rees algebra in terms of its primary
components. If the primary components of a monomial ideal are normal, we
present a simple procedure to compute its symbolic Rees algebra using Hilbert
bases, and give necessary and sufficient conditions for the equality between
its ordinary and symbolic powers. We give an effective characterization of the
Cohen--Macaulay vertex-weighted oriented forests. For edge ideals of transitive
weighted oriented graphs we show that Alexander duality holds. It is shown that
edge ideals of weighted acyclic tournaments are Cohen--Macaulay and satisfy
Alexander dualityComment: Special volume dedicated to Professor Antonio Campillo, Springer, to
appea