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CATEGORIES:Junior Geometry Seminar
SUMMARY:CscK-metrics and projective embeddings - Julien Me
yer (Université Libre de Bruxelles)
DTSTART;TZID=Europe/London:20140507T150000
DTEND;TZID=Europe/London:20140507T160000
UID:TALK52563AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52563
DESCRIPTION:Let $L$ be an ample line bundle over a compact Käh
ler manifold $X$. For each $k$ sufficiently large
one gets an embedding of $X$ into complex projecti
ve space by choosing a basis of $H^0(X\,L^k)$. Pul
ling back the Fubini-Study metric by these embeddi
ngs defines a sequence of "projective" Kähler metr
ics $\\omega_k& on $X$. A fundamental theorem by T
ian says that for convenient choices of basis\, th
is sequence converges back to the original Kähler
metric. Now it is natural to ask if any objects st
udied in Kähler geometry can be approximated by ob
jects from projective geometry.\nIn the talk I wil
l mainly focus on how cscK-metrics are approximate
d by so-called balanced metrics and how Calabi flo
w\, whose aim is to find cscK-metrics\, is approxi
mated by balancing flow. This is work by Donaldson
for the metrics and Fine for the flows.
LOCATION:MR20
CONTACT:Ruadhai Dervan
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