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Fakultät für Mathematik Universität Regensburg
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Seminar über Kähler-Geometrie/Seminar on Kähler
geometry
Semester
WiSe 2017 / 18

Lecturer
Bernd Ammann

Type of course (Veranstaltungsart)
Seminar

Contents
Kähler manifolds are complex manifolds together with a compatible Riemannian metric. Complex structures on a manifold M are expressed by a section J∈End(TM) satisfying J2=-1, and compatibility with a metric means that ω(X,Y):=g(X,Y) defines a symplectic struture on M. The simplest example is Cm with the standard complex structure and its standard metric.
The main subjects of the seminar are complex manifolds, holomorphic bundles, (p,q)-forms, blowups, Kähler manifolds, Laplace operators, and Hodge theory and Dolbeault theory. We will probably follow Moroianu's book cited below for this part.
Depending on the interests of the participants, we might consider some more advanced topics in the last part of the seminar. Er refer to the webpage for more details.

Literature
  • Andrei Moroianu, Lectures on Kähler geometry, London Math. Soc., Student texts 69
  • Werner Ballmann, Lectures on Kähler geometry, ESI Lectures in Mathematics and Physics, EMS, available in Regensburg as Ebook.


Recommended previous knowledge
For participation it is helpful to have followed an introductory lecture into differential geometry. It is also recommended to follow my lecture on symplectic manifolds during the winter term. We will not use many results from these lectures, but some experience with manifolds and vector bundles is important for understanding the subject.

Time/Date
Mo 16-18

Location
M102

Course homepage
http://www.mathematik.uni-regensburg.de/ammann/lehre/2017w_kaehler/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Organisational meeting/distribution of topics: Tuesday August 1st, 13:30, Sitzungszimmer
    Mathematik
  • Interested participants joining after August 1st shall send an email to Bernd Ammann. All
    participants are asked to register on GRIPS as we will send short time announcement via GRIPS.
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung
Modules
BV, BSem, MV, MSem, LA-GySem

ECTS
Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn
vor WS 15/16
Druckansicht