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Results tagged with at.algebraic-topology
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user 3377
Homotopy theory, homological algebra, algebraic treatments of manifolds.
10
votes
How restrictive is having zero Chern numbers for a compact complex manifold ? Same for negat...
When a compact Kahler manifold satisfies $c_1=0$, it admits a Ricci-flat Kahler metric by Calabi-Yau, hence its tangent bundle is polystable (direct sum of stable bundles of the same slope). Then its …
- 9,237
8
votes
Accepted
Proper family deformation retracts onto special fiber
Here is the reference:
Persson, Ulf,
On degenerations of algebraic surfaces,
Mem. Amer. Math. Soc. 11 (1977), no. 189.
Clemens, C. H. Degeneration of Kähler manifolds. Duke Math. J. 44 (1977), no. …
- 9,237
4
votes
Accepted
Hodge isometry sending the Kahler class to its opposite
It is impossible, because the birational (movable) nef cone is mapped to birational nef cone, where birational nef cone is a cone of all classes which are non-negative on all curves which move in fami …
- 9,237
8
votes
Hodge dual of de Rham cohomology and singular cohomology
The Hodge * operator action on cohomology is generally speaking
metric-dependent, hence * is not well-defined without fixing the metric.
There are some caveats. On complex curves, for example, the
Hod …
- 9,237
6
votes
0
answers
191
views
Isotopy classes of $CP^1$ in 4-manifolds
Let $S_1$, $S_2$ be homologous embedded 2-spheres
in a compact smooth 4-manifold. Under which additional
conditions are they smoothly isotopic? I am interested
in the state of the art picture when $S_ …
- 9,237