Timeline for Uniformity of injectivity for maps associated to linear systems
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2011 at 19:28 | comment | added | diverietti | So, where is Angelo's answer incorrect? I cannot see! | |
| Dec 16, 2011 at 10:33 | comment | added | Parsa | If the assumption is that for any $x,y \in X$ there is a global section such that it vanishes at $x$ and doesn't vanish at $y$, OR vice versa, then this system is not necessarily ample. | |
| Dec 14, 2011 at 14:58 | vote | accept | diverietti | ||
| Dec 14, 2011 at 14:38 | comment | added | Angelo | I have no idea how to give a direct elementary proof, sorry. | |
| Dec 14, 2011 at 14:36 | history | edited | Angelo | CC BY-SA 3.0 |
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| Dec 14, 2011 at 14:17 | comment | added | diverietti | I didn't say that in the original question, but I was really guessing if there was a "down-to-earth proof" of this fact... | |
| Dec 14, 2011 at 14:16 | comment | added | diverietti | Dear Angelo, thank you very much for your answer! As long as I can see, it seems to work perfectly. Two comments are in order: 1) Which "kind" of GAGA are you invoking here? Does one need $X$ to be already projective in order to say that a line bundle on $X$ pullback of an ample by a finite map is ample? 2) Do you think there is a more "elementary" proof of this fact? By elementary I mean just using, for example, combining sections of different powers of $L$ to obtain such an uniformity (I don't know if I am clear enough to make you understand what I mean by elementary here...) | |
| Dec 14, 2011 at 13:58 | history | answered | Angelo | CC BY-SA 3.0 |