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Results tagged with kahler-manifolds
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user 14037
Questions about Kähler manifolds and Kähler metrics.
6
votes
Accepted
Fujiki class $\mathcal C$ with a symplectic structure
If $X'$ is a Mukai flop of a compact hyper-Kähler manifold $X$, then $X'$ is in Fujiki class $\mathcal{C}$ and carries a holomorphic symplectic form $\sigma$. Taking the real part or the imaginary par …
- 1,829
3
votes
Accepted
Inequality on Kähler classes
Here is a simple proof using Theorem 1.6.1 in Lazarsfeld book, which is the following:
Theorem (Demailly)
If $H_1,\ldots,H_n$ are Kähler classes in a compact Kähler manifold of dimension $n$, then th …
- 1,829
3
votes
Is Kähler current class representable by semipositive forms?
This is an answer to your last question.
In general we can't represent the class of a Kähler current by a semi-positive smooth form $\alpha$.
Consider the blowup $\tilde{S} \to S$ of a compact Kähler …
- 1,829
2
votes
Do all symmetries of a Kähler quotient come from the original space?
Let $f : M \to E$ be a line bundle over an elliptic curve such that $\deg(M)<0$
and let $G = \mathbf{C}^*$ act on $M$ (on the left) by scalar multiplications. The maximal compact subgroup $K$ of $G$ …
- 1,829