Course description
Main contents of the course:
The Hodge decomposition theorem on Kähler manifolds
The Uniformisation theorem
The existence of Kähler-Einstein metrics on canonically polarised/Calabi-Yau manifolds
The classical Futaki invariant as an obstruction to the existence of constant scalar curvature Kähler (cscK) metrics
The LeBrun-Simanca openness theorem for cscK/extremal metrics
The infinite dimensional moment map picture for the scalar curvature and K-stability as an obstruction to the existence of cscK metrics
The Hitchin-Kobayashi correspondence for holomorphic vector bundles
Requirements and Selection
Entry requirements
Some basic differential geometry and complex geometry. Some experience with (elliptic) PDEs preferable, but we will go over the key points needed for our purposes in the lectures. Some parts of the course will feature some algebraic geometry, but this will be more focused on the ideas rather than precise proofs, so no real background with algebraic geometry is necessary.
Selection
Not relevant
Course syllabus
NFMV025
Department
Department of Mathematical Sciences
Subject
Natural Science and Mathematics
Type of course
Subject area course
Keywords
Kähler manifolds, metrics
