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Results tagged with kahler-manifolds
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user 391
Questions about Kähler manifolds and Kähler metrics.
9
votes
Structure of Kähler cone
Flag manifolds $G/B$ are nice: the Kähler cone is the positive Weyl chamber, with edges coming from the Poincaré duals of the Schubert divisors.
- 27.9k
4
votes
Accepted
Unique Equivariant Symplectic Structure for the Full Flag Manifold of $SU(3)$?
If $G$ acts on $M$ (both compact and finite-dimensional) preserving the symplectic form, and $M$ is simply-connected, the action is Hamiltonian. Then $M$ maps symplectomorphically to a coadjoint orbit …
- 27.9k
4
votes
Compact Kaehler manifolds that are isomorphic as symplectic manifolds but not as complex man...
If $M \to X$ is smooth and proper, and $M$ is K\"ahler, then the fibers are all symplectomorphic. (Proof: the Levi-Civita connection generates symplectomorphisms.) The family of elliptic curves was al …
- 27.9k
3
votes
Accepted
Condition on moment polytope for a toric manifold to be Fano
The basic answer is "yes, of course, because the toric variety is uniquely determined by the polytope. But no, because it's the wrong polytope for the question of Fanoness."
The question is whether t …
- 27.9k