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SUMMARY:holomorphic tubular neiborhood and meromorphic vector fields
DTSTART:20260703T083000Z
DTEND:20260703T103000Z
DTSTAMP:20260911T162700Z
UID:indico-event-16587@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hamza Bakhouch\n\nIt is known that the existence of 
 a holomorphic tubular neighborhood of a compact submanifold of a compact 
 complex manifold is rare\; for example\, the classical theorem due to Van
  de Ven states that the only submanifolds of CP(n) that possess a holomor
 phic tubular neighborhood are the linear ones. However\, when X is a mero
 morphic vector field in a neighborhood of a submanifold S such that the a
 ssociated foliation leaves S invariant\, we show—by choosing the right 
 coordinates (admissible coordinates)—that X induces a meromorphic vector
  field X_{00} on the whole of the normal bundle of S\, and the new foliat
 ion leaves S invariant as well. Moreover\, our motivation for this constr
 uction comes from the study of polynomial complete vector fields on \\mat
 hbb{C}^n\, so the main focus is to understand the induced foliation on th
 e hyperplane at infinity (S)\, which happens to be equivalent to study th
 e restriction of the foliation induced by X_{00} to S. This talk is devot
 ed to give an idea about the construction\, as well as how it preserves t
 he character of the vector field\, mainly the semicompleteness\, and how 
 this construction will allow us to use some algebraic geometry tools for 
 work in progress.\n \n\nhttps://indico.math.cnrs.fr/event/16587/
URL:https://indico.math.cnrs.fr/event/16587/
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