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Hamiltonian systems, symplectic flows, classical integrable systems

1 vote
0 answers
97 views

Systematic way of finding balanced metrics

In several PDE involving metrics (like the Hermite-Einstein equation for vector bundles and the constant scalar curvature Kahler equation for manifolds) there is a notion along these lines - If a solu …
11 votes

What is a Futaki invariant, what is the intuition behind it, and why is it important?

The Futaki invariant $F(X,[\omega])$ is a quantity that needs two pieces of information on a compact complex manifold $M$. 1) A Kahler class $[\omega]$ 2) A holomorphic vector field $X$. It is an …
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