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TitleThe slopes determined by $n$ points in the plane.
Author(s) Jorge Martin Morales
TypeArticle in Journal
AbstractLet m12, m13, , mn−1,n be the slopes of the (n2) lines connecting n points in general position in the plane. The ideal In of all algebraic relations among the mij defines a configuration space called the slope variety of the complete graph. We prove that In is reduced and Cohen-Macaulay, give an explicit Gröbner basis for it, and compute its Hilbert series combinatorially. We proceed chiefly by studying the associated Stanley-Reisner simplicial complex, which has an intricate recursive structure. In addition, we are able to answer many questions about the geometry of the slope variety by translating them into purely combinatorial problems concerning the enumeration of trees
ISSN0012-7094; 1547-7398/e
URL http://projecteuclid.org/euclid.dmj/1134666123
LanguageEnglish
JournalDuke Math. J.
Volume131
Number1
Pages119--165
PublisherDuke University Press, Durham, NC; University of North Carolina, Chapel Hill, NC
Year2006
Edition0
Translation No
Refereed No
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