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UID:6499@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210318T140000
DTEND;TZID=Europe/Paris:20210318T150000
DTSTAMP:20250118T133153Z
URL:https://www.i2m.univ-amu.fr/evenements/boundary-of-the-milnor-fiber-of
 -a-non-isolated-newton-non-degenerate-surface-singularity/
SUMMARY:Octave Curmi (Institut de Mathématiques Alfréd Rényi\, Budapest)
 : Boundary of the Milnor fiber of a non-isolated Newton non degenerate sur
 face singularity
DESCRIPTION:Octave Curmi: Milnor fibers play a crucial role in the study of
  the topology of a singularity of surface. They correspond to the differen
 t possible smoothings of the singularity. A description of the full fiber 
 is known in some particular cases\, but not in general\, even for isolated
  singularities. However\, the study of its boundary has been an active fie
 ld of research in the last decades. In different settings\, this boundary 
 has been proven to be a graph manifold. (Mumford\, 1961\, for isolated sin
 gularities\, Michel-Pichon\, 2003\, 2014\, for a smoothing of a reduced su
 rface with smooth total space\, Némethi-Szilard\, 2012\, with the same hy
 pothesis\, Bobadilla-Menegon Neto\, 2014\, for a non-reduced surface and a
  total space with isolated singularity).\nThe constructive proof provided 
 by Némethi and Szilard can be adapted to prove the same result for a smoo
 thing of a reduced surface with any total space. In the case when the tota
 l space is toric and the function giving the smoothing is Newton-non-degen
 erate\, we provide a combinatorial algorithm for the computation of the bo
 undary of the Milnor fiber.\nI will expose the main lines of this algorith
 m and some of the natural questions which it leads to.\nhttps://www.scienc
 edirect.com/science/article/abs/pii/S0001870820303078\n\nhttps://arxiv.org
 /abs/1911.13258\n\n&nbsp\;\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Octave_Curmi.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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