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TitleA non-regular Gr\"obner Fan.
Author(s) Anders N. Jensen
TypeArticle in Journal
AbstractThe Grobner fan of an ideal I⊂k[x1,,xn], defined by Mora and Robbiano, is a complex of polyhedral cones in ℝn. The maximal cones of the fan are in bijection with the distinct monomial initial ideals of I as the term order varies. If I is homogeneous the Grobner fan is complete and is the normal fan of the state polytope of I. In general the Grobner fan is not complete and therefore not the normal fan of a polytope. We may ask if the restricted Grobner fan, a subdivision of ℝn≥0, is regular, i.e. the normal fan of a polyhedron. The main result of this paper is an example of an ideal in n = 4 variables whose restricted Grobner fan is not regular.
ISSN0179-5376; 1432-0444/e
URL http://link.springer.com/article/10.1007%2Fs00454-006-1289-0
JournalDiscrete Comput. Geom.
PublisherSpringer US, New York, NY
Translation No
Refereed No