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SUMMARY:Asymptotics of hyperboilic\, Weil-Peterssen and Takhtajan-Zograf m
 etrics - Melrose\, R (Massachusetts Institute of Technology)
DTSTART:20150728T103000Z
DTEND:20150728T113000Z
UID:TALK60224@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:This will be a continuation of the talk by Xuwen Zhu on our jo
 int work concerning the regularity of the fibre hyperbolic metrics up to t
 he singular fibres for Lefschetz fibrations. In particular this applies to
  the universal curve over moduli space. I will discuss the marked case wit
 h the moduli space $mathcal{M}_{g\,n}$ of surfaces of genus $g$ with $n$ o
 rdered distinct points in the stable range\, $2g+nge3.$ As in the unmarked
  case the description of the regularity of the fibre hyperbolic metrics\, 
 up to the divisors forming the `boundary' of the Knudsen-Deligne-Mumford c
 ompactification\, implies boundary regularity for the Weil-Peterssen metri
 c. In this case it also leads to an asymptotic description of the Takhtaja
 n-Zograf  metric which contributes to the Chern form of the determinant bu
 ndle for $arpa$ on the fibres of the universal curve.\n
LOCATION:Seminar Room 1\, Newton Institute
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