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Results tagged with kahler-manifolds
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user 36974
Questions about Kähler manifolds and Kähler metrics.
0
votes
1
answer
310
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A question about a two form and a $(1,1)$ form on a compact Kähler manifold
Suppose $\omega$ is a real closed $(1,1)$ form on a compact Kähler manifold. If we have a real $d$-closed two form $\sigma$ such that $[\sigma]=[\omega] \in H^2(M)$, can we claim that this two form $\ …
- 593
3
votes
1
answer
439
views
A question about simply-connected homogeneous compact complex manifold
A result of Borel-Remmert in 1961/1962 published in Math. Ann. states that a compact homogeneous Kähler manifold must be the product of a complex torus and a projective-rational manifold. This implies …
- 593
2
votes
2
answers
502
views
A question about nef classes on compact Kähler manifolds
Suppose $M$ is a complex $n$-dimensioanl compact Kähler manifold and $\omega$ a Kähler class. Suppose $\alpha\in H^{1,1}(M,\mathbb{R})$ is a nef class belonging to the boundary of the Kähler cone of $ …
- 593
1
vote
1
answer
143
views
Upper bound of the dimension of automorphism group of compact Kähler manifolds
It is well-known that the dimension of the isometry group of an $n$-dimensional compact Riemannian manifold is no larger than $\frac{1}{2}n(n+1)$, which is attained precisely by $S^n$ and $\mathbb{R}P …
- 593