Cet ouvrage et des milliers d'autres font partie de la bibliothèque YouScribe
Obtenez un accès à la bibliothèque pour les lire en ligne
En savoir plus

Partagez cette publication

Vous aimerez aussi

ADDITIVE GROUP ACTIONS ON DANIELEWSKI VARIETIES AND THE CANCELLATION PROBLEM ADRIEN DUBOULOZ
PrepublicationdelInstitutFouriern o 680 (2005) www-fourier.ujf-grenoble.fr/prepublications.html Abstract. The cancellation problem asks if two complex algebraic varieties X and Y of the same dimension such that X  C and Y  C are isomorphic are isomorphic. Iitaka and Fujita [15] established that the answer is positive for a large class of varieties of any dimension. In 1989, Danielewski [4] constructed a famous counter-example using smooth ane surfaces with additive group actions. His construction was further generalized by Fieseler [10] and Wilkens [22] to describe a larger class of ane surfaces. Here we construct higher dimensional analogues of these surfaces. We study algebraic actions of the additive group C + on certain of these varieties, and we obtain counter-examples to the cancellation problem in every dimension n  2. Keywords : Danielewski varieties, Cancellation Problem, additive group actions, Makar-Limanov invariant.
Resume. Leproblemeditdesimpli cationdemandesideuxvarietesalgebriquescomplexes X et Y telles X  C et Y  C soientisomorphessontisomorphes.IitakaetFujitaontmontre ala ndesannees70quelareponseestarmativepourunelargeclassedevarietes.Les varietesanes-regleesnefontpaspartiedecetteclasse,et,en1989,Danielewskiaconstruit uncontre-exempleapartirdedeuxsurfacesanesdecetype.Danscetarticle,ongeneralise laconstructiondeDanielewskipourobtenirdesvarietesanesquisontlesespacestotauxde br es principaux sous le groupe additif, de base un schema non separe, en l’occurrence, un espaceanedontleshyperplansdecoordonnesonetemultiplies.Graˆceaunetechniquede deformationequivariantedeveloppeeparKalimanetMakar-Limanov,ondetermineensuite touteslesactionsdegroupesadditifssurcertainesdecesvarietes.Celaconduit nalementa desgeneralisationsnaturellesducontre-exampledeDanielewski,valablesentoutedimension n  2. Mots clefs :varietesdeDanielewski,ProblemedeSimpli cation,groupesadditifs,invariant de Makar-Limanov. Mathematics Subject Classi cation (2000) : 14R10,14R20.
1