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Combinatorics of binomial primary decomposition

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Abstract

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hypergeometric differential equations in several variables.

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Author notes

  1. Ezra Miller

    Present address: Department of Mathematics, Duke University, Durham, NC, 27708, USA

Authors and Affiliations

  1. Departamento de Matemática, FCEN, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina

    Alicia Dickenstein

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Laura Felicia Matusevich

  3. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Ezra Miller

Authors
  1. Alicia Dickenstein
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  2. Laura Felicia Matusevich
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  3. Ezra Miller
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Corresponding author

Correspondence to Laura Felicia Matusevich.

Additional information

A. Dickenstein was partially supported by UBACYT X064, CONICET PIP 5617 and ANPCyT PICT 20569, Argentina. L. F. Matusevich was partially supported by an NSF Postdoctoral Research Fellowship and NSF grant DMS-0703866. E. Miller was partially supported by NSF grants DMS-0304789 and DMS-0449102.

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Dickenstein, A., Matusevich, L.F. & Miller, E. Combinatorics of binomial primary decomposition. Math. Z. 264, 745–763 (2010). https://doi.org/10.1007/s00209-009-0487-x

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  • DOI: https://doi.org/10.1007/s00209-009-0487-x

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