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UID:6842@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200123T140000
DTEND;TZID=Europe/Paris:20200123T150000
DTSTAMP:20250118T133408Z
URL:https://www.i2m.univ-amu.fr/evenements/dirk-siersma-polar-degree-in-th
 e-presence-of-singularities/
SUMMARY: (...): Dirk SIERSMA - Polar degree in the presence of singularitie
 s
DESCRIPTION:: Dirk SIERSMA (Universiteit Utrecht)\n\nFor any projective hyp
 ersurface V:={f=0}\, the notion of polar degree is defined as the topologi
 cal degree of the (projectivized) gradient mapping of the homogeneous poly
 nomial f:\nGrad(f) : P^{n}Sing(V) --&gt\; P^{n}.\nThus pol(V) := Card(Grad
 (f)^{-1}(a)) for any generic point a.\nWe will discuss first the history o
 f polar degree and give several examples\, e.g. the determinant hypersurfa
 ce has polar degree 1\, which means the gradient map is bi-rational. The h
 ypersurfaces with pol(V)=1 are called homaloidal and are of extra interest
 .\nThe case that pol(V)=0 is related to the question what happens if the H
 essian of f is identically zero. This was solved by Gordan and Noether in 
 1876.\nDolgacev classified in 2000 all the projective homoloidal plane cur
 ves: a short list. Huh determined in 2014 all homoloidal hypersurfaces wit
 h at most isolated singularities.\nIn this talk we will reprove Huh's resu
 lts with methods of singularity theory. Moreover we will prove the conject
 ure of Huh that his list of polar degree 2 surfaces with isolated singular
 ities is complete! Finally we say something more about hypersurfaces with 
 the non-isolated singularities.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Dirk_Siersma.jpg
CATEGORIES:Groupe de travail,Singularités
LOCATION:St Charles - FRUMAM\, 3\, place Victor Hugo\, Marseille\, 13003\, 
 France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3\, place Victor Hugo\, Mar
 seille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=St Charles - FRUMAM:geo
 :0,0
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DTSTART:20191027T020000
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