Timeline for Measure in $\mathbb {C} ^p$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2020 at 16:38 | history | edited | Incnis Mrsi | CC BY-SA 4.0 |
oops, it is metric, not volume form
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| Nov 22, 2020 at 16:27 | comment | added | Incnis Mrsi | Oops, Ī̲ missed that $X$ is not (necessarily) one-dimensional. | |
| Nov 22, 2020 at 16:24 | comment | added | Ben McKay | But I agree that the question is too elementary. | |
| Nov 22, 2020 at 16:24 | comment | added | Ben McKay | The construction is not impossible; in fact it always well defined and always produces a measure, perhaps the zero measure. Your example produces the zero measure, since $\omega^2=0$ on $\mathbb{C}$. But on the other hand, other examples produce nonzero measures: if $f$ is any holomorphic map of $\mathbb{C}^p$, somewhere of full rank, and $X=\mathbb{C}^p$ and we take $\omega$ any Kaehler form, we get a measure $f^*\omega^p$ which is positive on any open set. | |
| Nov 22, 2020 at 16:10 | history | answered | Incnis Mrsi | CC BY-SA 4.0 |