• DOI:10.1215/s0012-7094-96-08401-x
• Corpus ID: 119712983

Binomial Ideals

@inproceedings{Eisenbud1994BinomialI,
  title={Binomial Ideals},
  author={David Eisenbud and Bernd Sturmfels},
  year={1994}
}

• D. Eisenbud, B. Sturmfels
• Published 11 January 1994
• Mathematics

: We investigate the structure of ideals generated by binomials (poly-nomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and it has numerous applications within and beyond pure mathematics. The ideals defining toric varieties are precisely the binomial prime ideals. Our main results concern primary decomposition: If I is a binomial ideal then the radical, associated primes, and isolated primary components of I are again binomial, and I admits primary decompositions in terms of binomial primary ideals. A geometric characterization is given for the affine algebraic sets that can be defined by binomials. Our structural results yield sparsity-preserving algorithms for finding the radical and primary decomposition of a binomial ideal.