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UID:7148@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190114T140000
DTEND;TZID=Europe/Paris:20190114T150000
DTSTAMP:20241120T203432Z
URL:https://www.i2m.univ-amu.fr/evenements/equivariant-embeddings-of-ratio
 nal-homology-balls/
SUMMARY:Brendan Owens (University of Glasgow): Equivariant embeddings of ra
 tional homology balls
DESCRIPTION:Brendan Owens: I will describe a family of smooth rational homo
 logy 4-balls B_{p\,q}\, bounded by lens spaces\; these are the Milnor fibr
 es of Wahl singularities. Smooth embeddings of B_{p\,q} in other 4-manifol
 ds arise in several contexts\, for example in smoothings of singular proje
 ctive varieties or in the rational blowdown surgery of Fintushel-Stern and
  J. Park. Khodorovskiy used Kirby calculus to give existence theorems for 
 such embeddings\, and these were generalised by Park-Park-Shin using metho
 ds from the minimal model program for algebraic 3-folds. Evans-Smith gave 
 a beautiful result showing that the symplectic embeddings of B_{p\,q} in t
 he complex projective plane correspond to solutions of the Markov equation
 \; this coincides precisely with a classification by Hacking-Prokhorov of 
 projective surfaces with quotient singularities which admit a CP^2 smoothi
 ng.\nI will describe a method for embedding B_{p\,q} by taking double bran
 ched covers of surfaces in the 4-ball. This recovers the results of Khodor
 ovskiy and Park-Park-Shin and also gives some interesting new embeddings. 
 In particular we find that there are more smooth embeddings in CP^2 than t
 hose of Hacking-Prokhorov and Evans-Smith.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 019/01/Brendan_Owens.jpg
CATEGORIES:Séminaire,Dynamique et Topologie
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