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Results tagged with complex-geometry
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user 26522
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.
8
votes
0
answers
288
views
Are the Chern numbers of a hyperbolic-type compact complex manifold bounded in terms of the ...
Let $X$ be an $n$-dimensional compact Kahler manifold with negative first Chern class. Are its Chern numbers $\prod_{i=1}^{n-1} c_i^{k_i}$, over $k _i
\geq 0$ with $\sum ik_i = n$, bounded in terms o …
7
votes
Complex Geometry Consequences of Serre's Kähler-Zeta Function
This is a purity result for a polarized Kähler dynamical system. The precise statement is that if $(X,\omega)$ is compact Kähler and $\phi : X \to X$ an endomorphism having the class $[\omega] \in H^2 …
- 13.8k
6
votes
1
answer
536
views
Generalizations of de Franchis and function field Mordell
The classical de Franchis theorem, as generalized by S. Kobayashi and T. Ochiai ("Meromorphic mappings onto compact complex spaces of general type," Inventiones, 1975), states that if $X$ is a complex …
- 13.8k
3
votes
0
answers
173
views
If a compact real submanifold of $\mathbb{CP}^n$ is approximable by complex algebraic curves...
To make this into a separate question:
If the supports of a sequence of complex algebraic curves in $\mathbb{CP}^n$ (images of non-constant holomorphic maps from compact Riemann surfaces) converge to …
- 13.8k