The Graph of Monomial Ideals
Klaus Altmann, Bernd Sturmfels
Abstract
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gröbner 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.
Create a lesson
Related papers
On the Stable category of maximal Cohen-Macaulay modules over Gorenstein rings-II
Tony J. Puthenpurakal
Symbolic powers of the ideal ofn general points in Pn-1
Ralf Fröberg, Boris Shapiro
Density functions for filtrations of graded ideals
Suprajo Das, Hoang Le Truong
Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring
Liang Chen
A criterion for determinantal presentations of numerical semigroup rings
Satoshi Murai, Kou Takahashi
Normality of ideals beyond the standard graded setting: families from numerical semigroup rings
Naoyuki Matsuoka