Timeline for Pushforward of a very ample line bundle on a curve to $\mathbb{P}^1$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2020 at 15:00 | comment | added | Donu Arapura | Good. That does it. | |
| Aug 11, 2020 at 14:39 | comment | added | abx | A vector bundle $E$ on $\mathbb{P}^1$ is of the form $\ \bigoplus \mathscr{O}_{\mathbb{P}^1}(e_i)\,$ with the $e_i$ positive if and only if $H^1(E(-2))=0$. If $E=p_*L$, this is equivalent to $H^1(L(-2p^*[0]))=0$. This will hold in particular as soon as $\deg L > 2g(C)-2+2k$. | |
| Aug 11, 2020 at 14:15 | history | edited | Donu Arapura | CC BY-SA 4.0 |
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| Aug 11, 2020 at 11:10 | comment | added | Li Li | Thanks for your answering. But I'm still wondered whether this is true if the condition is strenghened such that the degree of $L$ is sufficiently large. | |
| Aug 11, 2020 at 11:01 | vote | accept | Li Li | ||
| Aug 10, 2020 at 19:25 | history | edited | Donu Arapura | CC BY-SA 4.0 |
added 132 characters in body
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| Aug 10, 2020 at 18:55 | history | answered | Donu Arapura | CC BY-SA 4.0 |