Timeline for If $L$ is positive, $E\otimes L^k$ is Nakano positive for some $k$
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2013 at 4:49 | vote | accept | Michael Albanese | ||
| Aug 13, 2013 at 15:19 | history | edited | diverietti | CC BY-SA 3.0 |
added 2 characters in body
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| Aug 13, 2013 at 13:32 | comment | added | Michael Albanese | Upon first reading, it seems to check out, but I will have another read tomorrow and accept then. | |
| Aug 13, 2013 at 12:38 | comment | added | diverietti | Problem solved, I guess :) | |
| Aug 13, 2013 at 12:35 | history | edited | diverietti | CC BY-SA 3.0 |
Clarified and improved last argument
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| Aug 13, 2013 at 12:30 | comment | added | Michael Albanese | I've added some comments to the chat, but I haven't been able to resolve the problem. | |
| Aug 12, 2013 at 12:04 | history | edited | diverietti | CC BY-SA 3.0 |
nota bene added
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| Aug 12, 2013 at 9:54 | comment | added | diverietti | let us continue this discussion in chat | |
| Aug 12, 2013 at 8:02 | comment | added | diverietti | Yes, yes, I am sorry. I was a little bit fast. I'll fix it later! | |
| Aug 12, 2013 at 3:09 | comment | added | Michael Albanese | Why isn't $\theta_{E\otimes L^{\otimes k}} = \theta_E\otimes h_{L^{\otimes k}} + kh_E\otimes\theta_L$? Also, isn't $\theta_E$ a hermitian form on $T_X\otimes E$ not $T_X\otimes E\otimes L^{\otimes k}$? | |
| Aug 12, 2013 at 2:33 | comment | added | Michael Albanese | You say that $m_1 > 0$ by compactness. Compactness guarantees that $m_1$ exists; $m_1 > 0$ as $h_1$ is positive definite. Without compactness, you could try defining $m_1$ to be the infimum of $h_1$, but then we could only say $m_1 \geq 0$. | |
| Aug 11, 2013 at 16:53 | vote | accept | Michael Albanese | ||
| Aug 12, 2013 at 10:06 | |||||
| Aug 11, 2013 at 16:39 | comment | added | diverietti | Glad that you are satisfied! | |
| Aug 11, 2013 at 16:35 | comment | added | Michael Albanese | Fantastic. I was looking at using the sphere bundle (as can be seen from my last MSE question), but I couldn't quite get it to work. I was trying to take the sphere bundles associated to $T_X$, $E$ and $L^{\otimes k}$ respectively, rather than the bundle $T_X\otimes E\otimes L^{\otimes k}$. This led to problems when dealing with tensors with rank greater than one. | |
| Aug 11, 2013 at 16:24 | history | edited | diverietti | CC BY-SA 3.0 |
added 7 characters in body
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| Aug 11, 2013 at 16:23 | comment | added | diverietti | Yes, thanks!! I'll edit it! (Hola little brother, where are you?!) | |
| Aug 11, 2013 at 15:54 | comment | added | Gunnar Þór Magnússon | "by definition $m_1 > 0$" should maybe be by compactness? (Hola big brother!) | |
| Aug 11, 2013 at 15:42 | history | answered | diverietti | CC BY-SA 3.0 |