Timeline for Non-Kähler complex structure on $S^2 \times T^4$
Current License: CC BY-SA 4.0
4 events
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| Nov 28, 2023 at 17:11 | comment | added | V. Rogov | Your construction always gives rise to a complex manifold $M$ which is a holomorphic principal bundle over $\mathbb{CP}^1$. In particular, the family of complex tori over $\mathbb{CP}^1$ is isotrivial. As Michael suggests, you can take the twistor space, then the family will not be isotrivial, so it does not come from this construction. It would be interesting to ask if there exists a complex structure on $M$ such that $M$ does not fibre over $\mathbb{CP}^1$. | |
| Nov 21, 2023 at 9:31 | comment | added | Michael Albanese | Another example to consider is the twistor space of $T^4$ with a flat metric. | |
| Nov 18, 2023 at 3:26 | history | edited | Chicken feed | CC BY-SA 4.0 |
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| Nov 18, 2023 at 3:00 | history | asked | Chicken feed | CC BY-SA 4.0 |