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SUMMARY:CscK-metrics and projective embeddings - Julien Meyer (Université
  Libre de Bruxelles)
DTSTART:20140507T140000Z
DTEND:20140507T150000Z
UID:TALK52563@talks.cam.ac.uk
CONTACT:Ruadhai Dervan
DESCRIPTION:Let $L$ be an ample line bundle over a compact Kähler manifol
 d $X$. For each $k$ sufficiently large one gets an embedding of $X$ into c
 omplex projective space by choosing a basis of $H^0(X\,L^k)$. Pulling back
  the Fubini-Study metric by these embeddings defines a sequence of "projec
 tive" Kähler metrics $\\omega_k& on $X$. A fundamental theorem by Tian sa
 ys that for convenient choices of basis\, this sequence converges back to 
 the original Kähler metric. Now it is natural to ask if any objects studi
 ed in Kähler geometry can be approximated by objects from projective geom
 etry.\nIn the talk I will mainly focus on how cscK-metrics are approximate
 d by so-called balanced metrics and how Calabi flow\, whose aim is to find
  cscK-metrics\, is approximated by balancing flow. This is work by Donalds
 on for the metrics and Fine for the flows.
LOCATION:MR20
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