 
Summary: Journal of Pure and Applied Algebra 201 (2005) 250263
www.elsevier.com/locate/jpaa
The graph of monomial ideals
Klaus Altmanna
, Bernd Sturmfelsb,
aFB Mathematik und Informatik, WE2, Freie Universität Berlin, Arnimallee 3, D14195 Berlin, Germany
bDepartment of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA
Received 12 September 2002
Available online 7 April 2005
Dedicated to Wolmer Vasconcelos on the occasion of his 65th birthday
Abstract
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 squarefree monomial ideals. In the latter
case, the edges correspond to generalized bistellar flips.
© 2005 Elsevier B.V. All rights reserved.
MSC: 13P10; 14B07
1. Edge ideals
The most important tool for computing with ideals in a polynomial ring K[x] =
