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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Nodal curves old and new - Thomas\, RPW (Imperial)
DTSTART;TZID=Europe/London:20110311T151500
DTEND;TZID=Europe/London:20110311T161500
UID:TALK30202AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30202
DESCRIPTION:I will describe a classical problem going back to 
 1848 (Steiner\, Cayley\, Salmon\,...) and a soluti
 on using simple techniques\, but techniques that o
 ne would never really have thought of without idea
 s coming from string theory (Gromov-Witten invaria
 nts\, BPS states) and modern geometry (the Maulik-
 Nekrasov-Okounkov-Pandharipande conjecture). In ge
 neric families of curves C on a complex surface S\
 , nodal curves -- those with the simplest possible
  singularities -- appear in codimension 1. More ge
 nerally those with d nodes occur in codimension d.
  In particular a d-dimensional linear family of cu
 rves should contain a finite number of such d-noda
 l curves. The classical problem -- at least in the
  case of S being the projective plane -- is to det
 ermine this number. The Gttsche conjecture states 
 that the answer should be topological\, given by a
  universal degree d polynomial in the four numbers
  C.C\, c_1(S).C\, c_1(S)^2 and c_2(S). There are n
 ow proofs in various settings\; a completely algeb
 raic proof was found recently by Tzeng. I will exp
 lain a simpler approach which is joint work with M
 artijn Kool and Vivek Shende.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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