# Tag Info

### Complex vector bundles on compact complex manifolds

This is an explanation of my comment above, namely: "Complex vector bundles over a CW complex of dimension $\leq 4$ are classified by their Chern classes and rank. Moreover, every possible choice ...
Accepted

### Examples of 6-manifolds without an almost complex structure

Turning comments into answer: An example of a closed 6-manifold not admitting an almost complex structure is $S^1 \times (SU(3)/SO(3))$. From the obstruction theory for lifting the map $M \to BSO(6)$ ...
Accepted

### Difference between stabilizer and automorphism group of subvariety of an abelian variety

They have absolutely no reason to be equal. Consider the case where $A$ is the Jacobian of a genus 2 curve $C$, and $X=C$ embedded in $A$ by $x\mapsto [x]-[p]$ for some fixed point $p\in C$. Then $X$ ...
• 34.3k

1 vote

### Fundamental groups of primitive non-algebraic compact Kähler manifolds

I am not sure how one checks primitivity for a compact Kähler manifold, this seems to be too delicate property. Intuitively speaking, very non-algebraic Kähler manifolds have very simple fundamental ...
• 758
1 vote

### Holomorphic vector fields acting on Dolbeault cohomology

Klemyatin proved that this action is trivial if the corresponding ${\Bbb C}$-flow is compatible with some metric (hence can be extended to a compact torus action), https://arxiv.org/abs/1909.04075, (N....
• 7,568

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