Skip to main content

# Questions tagged [kahler-manifolds]

Questions about Kähler manifolds and Kähler metrics.

534 questions
Filter by
Sorted by
Tagged with
2 votes
0 answers
33 views

### Is this the connection on the prequantum line bundle of a Kähler manifold?

Let $(\mathcal{L},\nabla,\langle\cdot,\cdot\rangle)\to (M,\omega,I)$ be a prequantum line bundle on a Kähler manifold. The so-called Bergman kernel (the integral kernel of the projection onto ...
• 1,218
3 votes
1 answer
116 views

### Locality of Kähler-Ricci flow

Let $(M,I, \omega)$ be a compact Kähler manifold with $c_1(M)=0$. Denote by $\operatorname{Ric}^{1,1}(\omega)$ the Ricci (1,1)-form, that is, the curvature of the canonical bundle. It is known ("...
• 9,157
4 votes
0 answers
95 views

### Can an amalgamated free product be a Kähler group?

A finitely generated group $\Gamma$ is called a Kähler group if there exists a closed Kähler manifold $X$ such that $\pi_1(X) = \Gamma$. Let $\Gamma = G_{\ast H}K$ be a non-trivial amalgamated free ...
• 504
3 votes
0 answers
104 views

### Relative $dd^c$-lemma

Let $f\colon X\to Y$ be a surjective map of compact Kähler varieties. Pick an open subset $U\subset Y$ and let $X_U$ be the preimage of $U$. Does the $dd^c$-lemma hold on $X_U$? Namely, let $\alpha$ ...
• 101
3 votes
1 answer
184 views

### A formula resembling the integral mean value on Kähler manifolds

I am reading comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces by John Lott. I have a problem when reading the proof of the following theorem: Theorem. ...
• 173
5 votes
1 answer
149 views

• 113