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SUMMARY:Craig van Coevering (Boğaziçi)
DTSTART:20230414T124000Z
DTEND:20230414T134000Z
DTSTAMP:20260423T021247Z
UID:OBAGS/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/25/">E
 xtremal Kähler metrics and the moment map</a>\nby Craig van Coevering (Bo
 ğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
 t\nAn extremal Kähler metric is a canonical Kähler metric\, introduced b
 y E.\nCalabi\, which is somewhat more general than a constant scalar curva
 ture Kähler metric. The existence of such a metric is an ongoing research
  subject and expected to be equivalent to some form of geometric stability
  of the underlying polarized complex manifold $(M\, J\, [\\omega])$ –the
  Yau-Tian-Donaldson  Conjecture. Thus it is no surprise that there is a mo
 ment map\, the scalar curvature (A. Fujiki\, S. Donaldson)\, and the probl
 em can be described as an infinite dimensional version of the familiar fin
 ite dimensional G.I.T.\n\nI will describe how the moment map can be used t
 o describe the local space of extremal metrics on a symplectic manifold. E
 ssentially\, the local picture can be reduced to finite dimensional G.I.T.
  In particular\, we can construct a course moduli space of extremal Kähle
 r metrics with a fixed polarization $[\\omega] \\in  H^2(M\, \\mathbb{R})$
 \, which is an Hausdorff complex analytic space\n
LOCATION:https://researchseminars.org/talk/OBAGS/25/
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