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Results tagged with complex-geometry
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user 19071
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
3
votes
1
answer
458
views
A question about the existence of a constant scalar curvature metric on $\mathbb{C}P^n\#\ove...
We know that Calabi constructed some extremal metrics on $\mathbb{C}P^n\#\overline{\mathbb{C}P^n}$ which are not constant scalar curvature ones.
I just want to know given a Kähler class in $\mathbb{ …
- 19.3k
4
votes
0
answers
389
views
The existence of compact Kähler manifolds satisfying $h^{1,1}=h^{2,2}$
Recently I have been thinking about a problem. During this process I faced a phenomenon which is related to those Kähler manifolds whose Hodge numbers satisfy $h^{1,1}=h^{2,2}$. Except $\mathbf{CP}^n$ …
- 25.8k
3
votes
1
answer
879
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What does the Kähler cone of the one-point blow-up of $\mathbb{C}P^n$ look like?
I found that related to the Kähler cone there are many discussions on MathOverflow.
Recently I am interested in the very special manifold of the one-point blow up of $\mathbb{C}P^n$ and just want to …
- 6,210
2
votes
1
answer
557
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the existence of compact Kahler manifolds satisfying some Hodge numbers' restrictions
Given any $n\geq 2$, is there an example of $n$-dimensional compact Kahler manifold such that its Hodge numbers satisfy $h^{1,1} = h^{2,2} < h^{3,3} = h^{4,4} < h^{5,5} = h^{6,6} < \cdots h^{[\frac{n} …
- 19.3k
5
votes
1
answer
464
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infimum of the Calabi energy in a given Kahler class
Given a compact Kahler manifold $M^n$ and a Kahler class $\Omega$. We have the Calabi energy (or Calabi functional)
$$\textrm{Ca}(\omega)=\int_Ms^2(\omega)\omega^n,\qquad \forall \omega\in\Omega.$$
H …
- 6,871
1
vote
1
answer
668
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about Kahler curvature tensor on page 77 of Besse's book "Einstein Manifolds"
We know that Kahler curvature tensor can be decomposed into three items:scalar part, traceless Ricci part and Bochner curvature tensor. In page 77 of Besse's book, it appears two symbols: $B$ and $B_0 …
- 108k