{"title":"Equivalence problem for minimal rational curves with isotrivial varieties of minimal rational tangents","authors":"Jun-Muk Hwang","doi":"10.24033/ASENS.2129","DOIUrl":"https://doi.org/10.24033/ASENS.2129","url":null,"abstract":"Nous enoncons le probleme d'equivalence, au sens de E. Cartan, pour des familles de courbes rationnelles minimales sur des varietes projectives unireglees. Un invariant important de ce probleme d'equivalence est la variete des tangentes rationnelles minimales. Nous etudions le cas ou les varietes de tangentes rationnelles minimales aux points generiques forment une famille isotriviale. La question principale dans ce cas est: pour quelle variete projective Z une famille de courbes rationnelles minimales, dont les varietes de tangentes rationnelles minimales sont Z-isotriviales, est-elle localement equivalente au modele plat? Nous montrons que c'est le cas lorsque Z verifie certaines conditions de geometrie projective qui sont satisfaites pour une hypersurface non singuliere de degre > 4.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"33 1","pages":"607-620"},"PeriodicalIF":1.9,"publicationDate":"2009-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80781899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"FANO MANIFOLDS OF DEGREE TEN AND EPW SEXTICS","authors":"A. Iliev, L. Manivel","doi":"10.24033/ASENS.2146","DOIUrl":"https://doi.org/10.24033/ASENS.2146","url":null,"abstract":"O'Grady a demontre que certaines sextiques speciales dans ℙ 5 , les sextiques EPW, admettent pour revetements doubles des varietes symplectiques holomorphes lisses. Nous proposons une nouvelle approche de ces varietes symplectiques, en montrant qu'elles se construisent a partir des schemas de Hilbert de coniques sur des varietes de Fano de dimension quatre et de degre dix. En guise d'application, nous construisons des familles de surfaces lagrangiennes dans ces varietes symplectiques, puis des systemes integrables dont les fibres sont des jacobiennes intermediaires.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"26 1","pages":"393-426"},"PeriodicalIF":1.9,"publicationDate":"2009-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84843672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds","authors":"L. Meersseman","doi":"10.24033/asens.2148","DOIUrl":"https://doi.org/10.24033/asens.2148","url":null,"abstract":"Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in $Bbb C^p$, for some $p>0$) or differentiable (parametrized by an open neighborhood of $0$ in $Bbb R^p$, for some $p>0$) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions are the two families locally isomorphic at 0? In this article, we give a sufficient condition in the case of holomorphic families. We show then that, surprisingly, this condition is not sufficient in the case of differentiable families. We also describe different types of counterexamples and give some elements of classification of the counterexamples. These results rely on a geometric study of the Kuranishi space of a compact complex manifold.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"24 1","pages":"495-525"},"PeriodicalIF":1.9,"publicationDate":"2009-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88334289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-orbit equivalent actions of $mathbb {F}_n$","authors":"A. Ioana","doi":"10.24033/ASENS.2106","DOIUrl":"https://doi.org/10.24033/ASENS.2106","url":null,"abstract":"For any 2 ≤ n ≤ ∞, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group F_n. These actions arise as diagonal products between a generalized Bernoulli action and the action Fn ↷ (T^2, λ^2), where F_n is seen as a subgroup of SL_(2)(Z).","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"20 1","pages":"675-696"},"PeriodicalIF":1.9,"publicationDate":"2009-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83019922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Groupes de Cremona, connexité et simplicité","authors":"J. Blanc","doi":"10.24033/ASENS.2123","DOIUrl":"https://doi.org/10.24033/ASENS.2123","url":null,"abstract":"The Cremona group is connected in any dimension and, endowed with its topology, it is simple in dimension 2.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"71 1","pages":"357-364"},"PeriodicalIF":1.9,"publicationDate":"2009-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86239295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Le problème de Lehmer relatif en dimension supérieure","authors":"Emmanuel Delsinne","doi":"10.24033/ASENS.2114","DOIUrl":"https://doi.org/10.24033/ASENS.2114","url":null,"abstract":"Nous generalisons en dimension superieure un theoreme d'Amoroso et Zannier concernant le probleme de Lehmer relatif. Nous minorons la hauteur d'un point d'un tore en fonction de son indice d'obstruction sur ℚ ab , l'extension abelienne maximale de ℚ, a condition qu'il ne soit pas contenu dans une sous-variete de torsion de petit degre. Nous en deduisons une minoration du minimum essentiel d'une sous-variete non contenue dans un sous-groupe algebrique propre en fonction de son indice d'obstruction sur ℚ ab . Nous montrons ainsi, a un epsilon pres, les conjectures les plus fines qui peuvent etre formulees dans ce cadre.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"4 1","pages":"981-1028"},"PeriodicalIF":1.9,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73352176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiple zeta values and periods of moduli spaces $overline{mathfrak {M}}_{0,n}$","authors":"F. Brown","doi":"10.24033/ASENS.2099","DOIUrl":"https://doi.org/10.24033/ASENS.2099","url":null,"abstract":"Nous demontrons une conjecture de Goncharov et Manin qui predit que les periodes des espaces de modules M 0,n des courbes de genre 0 avec n points marques sont des valeurs zeta multiples. Nous introduisons une algebre differentielle de fonctions polylogarithmes multiples sur M 0,n dans laquelle il existe des primitives. L'idee principale est d'appliquer une version de la formule de Stokes recursivement pour reduire chaque integrale de periodes a une combinaison lineaire de valeurs zeta multiples. Nous donnons egalement une interpretation geometrique des double relations de melange pour les valeurs zeta multiples. En considerant des applications naturelles entre les espaces des modules, on deduit des formules de produit generales entre leurs periodes. Les doubles relations de melange s'obtiennent comme deux cas particuliers de cette construction.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"32 1","pages":"371-489"},"PeriodicalIF":1.9,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74596195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"$mathcal {D}$-modules arithmétiques surholonomes","authors":"Daniel Caro","doi":"10.24033/ASENS.2092","DOIUrl":"https://doi.org/10.24033/ASENS.2092","url":null,"abstract":"Soient k un corps parfait de caracteristique p > 0, U une variete sur k et F une puissance de Frobenius. Nous construisons la categorie des (F-)D-modules arithmetiques surholonomes sur U et celle des (F-)complexes de D-modules arithmetiques sur U surholonomes. Nous montrons que les complexes surholonomes sont stables par images directes, images inverses, images inverses extraordinaires, images directes extraordinaires, foncteurs duaux. De plus, lorsque U est lisse, nous verifions que les F-isocristaux surconvergents unites sur U sont surholonomes. Cela implique leur holonomie, ce qui prouve en partie une conjecture de Berthelot.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"1 1","pages":"141-192"},"PeriodicalIF":1.9,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72727506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Size Minimizing Surfaces","authors":"T. Pauw","doi":"10.24033/ASENS.2090","DOIUrl":"https://doi.org/10.24033/ASENS.2090","url":null,"abstract":"We prove a new existence theorem pertaining to the Plateau problem in 3-dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and WH. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"61 1","pages":"37-101"},"PeriodicalIF":1.9,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80870447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"HERMAN'S LAST GEOMETRIC THEOREM","authors":"B. Fayad, R. Krikorian","doi":"10.24033/ASENS.2093","DOIUrl":"https://doi.org/10.24033/ASENS.2093","url":null,"abstract":"Nous presentons une preuve du dernier theoreme geometrique d'Herman qui affirme que, si un diffeomorphisme F de l'anneau possede la propriete d'intersection, alors toute courbe C°° F-invariante, sur laquelle le nombre de rotation de F est diophantien, est accumulee par un ensemble de mesure positive de courbes invariantes C°° sur lesquelles F est C°° -conjuguee a une rotation. Ceci implique en particulier la stabilite des points fixes elliptiques diophantiens des diffeomorphismes du plan qui preservent l'aire. Le caractere remarquable de ce theoreme est qu'il ne requiert aucune condition de torsion.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"59 1","pages":"193-219"},"PeriodicalIF":1.9,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83998207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}