Monomial ideals and Cohen-Macaulay vertex-weighted digraphs

@inproceedings{Gimenez2017MonomialIA,
  title={Monomial ideals and Cohen-Macaulay vertex-weighted digraphs},
  author={Philippe Gimenez and Jose Eduardo Martinez-Bernal and Aron Simis and Rafael H. Villarreal and Carlos E. Vivares},
  year={2017}
}
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 that of its primary components. If the primary components of a monomial ideal are normal, we present a simple procedure to… CONTINUE READING

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