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SUMMARY:Octave Curmi (v): A new proof of Gabrielov’s rank Theorem
DTSTART;VALUE=DATE-TIME:20201203T100000Z
DTEND;VALUE=DATE-TIME:20201203T110000Z
DTSTAMP;VALUE=DATE-TIME:20210227T070941Z
UID:indico-event-5859@indico.math.cnrs.fr
DESCRIPTION:This talk concerns Gabrielov’s rank Theorem\, a fundamental
result in local complex and real-analytic geometry\, proved in the 1970’
s. Contrasting with the algebraic case\, it is not in general true that th
e analytic rank of an analytic map (that is\, the dimension of the analyti
c-Zariski closure of its image) is equal to the generic rank of the map (t
hat is\, the generic dimension of its image). This phenomenon is involved
in several pathological examples in local real-analytic geometry. Gabrielo
v’s rank Theorem provides a formal condition for the equality to hold.\n
\nDespite its importance\, the original proof is considered very difficult
. There is no alternative proof in the literature\, besides a work from To
ugeron\, which is itself considered very difficult. I will present a new w
ork in collaboration with André Belotto da Silva and Guillaume Rond\, wh
ere we provide a complete proof of Gabrielov’s rank Theorem\, for which
we develop formal-geometric techniques\, inspired by ideas from Gabrielov
and Tougeron\, which clarify the proof.\n\nI will start with some fundamen
tal examples of the phenomenon at hand\, and expose the main ingredients o
f the strategy of this difficult proof.\n\nhttps://indico.math.cnrs.fr/eve
nt/5859/
LOCATION:batiment I 001
URL:https://indico.math.cnrs.fr/event/5859/
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