Timeline for Divisors with positive Iitaka dimension
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 25, 2014 at 19:19 | comment | added | aegbert | There is the following lemma which might be useful (again this is in Lazarsfeld, Positivity, 2.1.38) Let $L$ a line bundle on a smooth variety, set $\kappa = \kappa(X,L)$. Then there are constants $a,A>0$ such that $a m^\kappa \le h^0(X,L^m) \le A m^\kappa$ for all sufficiently large $m\in \mathbb{N}(X,L)$. So if the exponent of your line bundle is $1$, for example if $L$ is big, then this might happen. | |
| Mar 25, 2014 at 10:12 | comment | added | Marcos Jardim | Thanks for the comments and examples! Do you know if the property of $n \to h^0(\cal{O}(nD))$ being strictly increasing has a special name in the literature? | |
| Mar 25, 2014 at 10:10 | vote | accept | Marcos Jardim | ||
| Mar 25, 2014 at 10:10 | vote | accept | Marcos Jardim | ||
| Mar 25, 2014 at 10:10 | |||||
| Mar 25, 2014 at 10:10 | vote | accept | Marcos Jardim | ||
| Mar 25, 2014 at 10:10 | |||||
| Mar 20, 2014 at 12:58 | history | edited | aegbert | CC BY-SA 3.0 |
Added additional info
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| Mar 20, 2014 at 12:25 | review | First posts | |||
| Mar 20, 2014 at 12:28 | |||||
| Mar 20, 2014 at 12:07 | history | answered | aegbert | CC BY-SA 3.0 |