The Graph of Monomial Ideals

Details The Graph of Monomial Ideals The Graph of Monomial Ideals

2002-09-12

arxiv.org/abs/math/0209152v1

Mathematics

Commutative Algebra

15 pages, Latex

Scientific paper

There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gr\"obner bases or the action of an algebraic torus. We present algorithms for computing the (affine schemes representing) edges in this graph. We study the induced subgraphs on multigraded Hilbert schemes and on square-free monomial ideals. In the latter case, the edges correspond to generalized bistellar flips.

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