The Graph of Monomial Ideals
نویسندگان
چکیده
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring K[x1, . . . , xn]. The definition involves Gröbner bases or the action of the algebraic torus (K∗)n. 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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