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تسجيل مستخدم جديدPresque toute surface K3 contient une infinite dhypersurfaces Levi-plates lineaires
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تأليف
Felix Lequen
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We investigate the construction of real analytic Levi-flat hypersurfaces in K3 surfaces. By taking images of real hyperplanes, one can construct such hypersurfaces in two-dimensional complex tori. We show that almost every K3 surfaces contains infinitely many Levi-flat hypersurfaces of this type. The proof relies mainly on a recent construction of Koike and Uehara, ideas of Verbitsky on ergodic complex structures, as well as an argument due to Ghys in the context of the study of the topology of generic leaves. -- On sinteresse `a la construction dhypersurfaces Levi-plates analytiques relles dans les surfaces K3. On peut en construire dans les tores complexes de dimension 2 en prenant des images dhyperplans reels. On montre que presque toute surface K3 contient une infinite dhypersurfaces Levi-plates de ce type. La preuve repose principalement sur une construction recente due `a Koike-Uehara, ainsi que sur les idees de Verbitsky sur les structures complexes ergodiques et une adaptation dun argument d^u `a Ghys dans le cadre de letude de la topologie des feuilles generiques.
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