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- W3212805655 abstract "We first study symplectically embedded curves in symplectic surfaces with high self-intersection numbers compared to their genus. We prove in two different ways that such a curve completely determines both the diffeomorphism type of the surface in which it is embedded and the embedding itself. The first proof uses Seiberg-Witten theory whereas the second one only involves pseudoholomorphic techniques. We deduce from this result that the contact $3$-manifolds naturally associated with those curves admit a unique strong symplectic filling up to diffeomorphism. We next examine symplectic sections of geometrically ruled complex surfaces over elliptic curves. We show that such a section is symplectically isotopic to a complex section. -- On 'etudie dans un premier temps les courbes symplectiquement plong'ees dans les surfaces symplectiques dont les nombres d'auto-intersection sont suffisamment grands par rapport leurs genres. On montre de deux mani`eres diff'erentes qu'une telle courbe d'etermine `a la fois la classe de diff'eomorphisme de la surface symplectique qui la contient et la mani`ere dont elle est plong'ee dans cette surface. La premi`ere d'emonstration fait appel `a la th'eorie de Seiberg-Witten, alors que la seconde se restreint aux techniques pseudoholomorphes. On d'eduit de ce r'esultat l'unicit'e `a diff'eomorphisme pr`es des remplissages symplectiques forts des vari'et'es de contact de dimension $3$ naturellement associ'ees `a ce type de courbes. Dans un second temps, on s'int'eresse aux sections symplectiques des surfaces complexes g'eom'etriquement r'egl'ees au-dessus de courbes elliptiques. On montre qu'une telle section est symplectiquement isotope `a une section complexe." @default.
- W3212805655 created "2021-11-22" @default.
- W3212805655 creator A5010110210 @default.
- W3212805655 date "2021-11-09" @default.
- W3212805655 modified "2023-09-27" @default.
- W3212805655 title "Courbes symplectiques de haute auto-intersection dans les surfaces symplectiques." @default.
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