A Toric Ring with Irrational Poincar E-betti Series
نویسندگان
چکیده
{ We show that there exists a toric curve in P 8 , whose homogeneous coordinate ring has a presentation with 12 quadratic relations and whose Poincar e-Betti series is irrational. The example was found by a computer search, aiming at a homological classiication of those toric curves that have a quadratic presentation in P n?1 for n 9. Some other consequences of this search are also presented. Un anneau toro dal a s erie de Poincar e-Betti irrationnelle R esum e.{ Nous montrons qu'il existe une courbe toro dale dans P 8 , dont l'anneau des coordonn ees ho-mog enes a une pr esentation avec 12 relations quadratiques, et dont la s erie de Poincar e-Betti est irrationnelle. Cet exemple a et e trouv e a l'aide d'une etude, faite sur ordinateur, dont le but a et e la classiication ho-mologique des courbes toro dales a relations quadratiques dans P n?1 pour n 9. D'autres cons equences de cette etude sont pr esent ees. Version frann caise abr eg ee | Soit M un sous-mono de de N d engendr e par n vecteurs a 1 ; : : :; a n ayant la m^ eme somme des coordonn ees. Soit k un corps. L'anneau toro dal kM] est la sous-alg ebre de l'anneau des polyn^ omes kz 1 ; : : :; z d ] engendr ee par les mon^ omes z ai = z ai1
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