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UID:3122@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191024T103000
DTEND;TZID=Europe/Paris:20191024T113000
DTSTAMP:20191009T083000Z
URL:https://www.i2m.univ-amu.fr/evenements/beatriz-molina-samper-invariant
 -surfaces-of-non-degenerate-foliations-in-dimension-three/
SUMMARY: (...): Beatriz MOLINA SAMPER - Invariant surfaces of non-degenerat
 e foliations in dimension three
DESCRIPTION:: Beatriz MOLINA SAMPER (Universidad de Valladolid)More than fo
 rty years ago the recognized mathematician Rene Thom asked the following q
 uestion : Is there always an invariant curve for a germ of foliation on (C
 2\, 0) ? In 1982 Cesar Camacho and Paulo Sad gave a positive answer to thi
 s question. For higher dimension\, there are results of Felipe Cano\, Domi
 nique Cerveau and Jean-Francois Mattei where they prove the existence of i
 nvariant hypersufaces for germs of foliations on (Cn\, 0)\, in the non-dic
 ritical frame. However\, when the existence of dicritical components in th
 e exceptional divisor is allowed\, the classical collection of examples of
  Jouanolou provides foliations in (C3\, 0) without invariant surface. We p
 resent here a result of existence of invariant surface for “non-degenera
 te foliations” on (C3\, 0)\, possibly dicritical. In this context\, with
  non-degenerated we mean foliations that admit a combinatorial procedure o
 f reduction of singularities (these generalize Kouchnirenko’s classical 
 non-degenerate hypersurfaces). To prove this assertion of local nature in 
 dimension three\, we pass through the following global statement in dimens
 ion two : “The isolated invariant branches of non-degenerate foliations 
 over projective toric surfaces extend to global curves”.http://www.resea
 rchgate.net/profile/Beatriz_Molina-Samper
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