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Results tagged with kahler-manifolds
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user 3709
Questions about Kähler manifolds and Kähler metrics.
3
votes
0
answers
235
views
Positive representatives of Chern classes
We say that a $(p,p)$-form on a smooth projectively variety $X$ of dimension $n$ is positive if its restriction to every $p$-dimensional subspace of the holomorphic tangent space at every point is a v …
- 3,383
4
votes
1
answer
215
views
Examples of surfaces with negative Kahler curvature operator
Compact ball quotients are examples of compact Kahler surfaces with negative curvature operator.
Are there any other examples ? What about nonpositive (other than the product of two Riemann surfaces …
- 3,383
3
votes
1
answer
286
views
Kähler classes for surfaces of general type with $c_1^2=3c_2$
Given a smooth, compact complex surface with ample canonical bundle satisfying $c_1^2=3c_2$, is it true that every Kahler class is a multiple of $c_1$? This seems to be the case for fake projective pl …
- 3,383
11
votes
What is a Futaki invariant, what is the intuition behind it, and why is it important?
The Futaki invariant $F(X,[\omega])$ is a quantity that needs two pieces of information on a compact complex manifold $M$.
1) A Kahler class $[\omega]$
2) A holomorphic vector field $X$.
It is an …
- 3,383