Timeline for Extending a prime divisor to a principal divisor
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2016 at 19:41 | history | edited | Shubhodip Mondal | CC BY-SA 3.0 |
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| May 25, 2016 at 4:28 | vote | accept | Shubhodip Mondal | ||
| May 24, 2016 at 18:08 | answer | added | Jason Starr | timeline score: 5 | |
| May 24, 2016 at 15:00 | comment | added | Hoot | If you want to see a really baby version of this I think Ex. IV.1.9 in Hartshorne is good. Of course, you said you already knew how to do curves and there are many more assumptions there, but still. | |
| May 24, 2016 at 14:03 | history | edited | Shubhodip Mondal | CC BY-SA 3.0 |
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| May 24, 2016 at 13:33 | comment | added | Shubhodip Mondal | @JasonStarr: Thanks a lot for your comment. Could you please hint at how X admitting an ample invertible sheaf helps to prove the result? | |
| May 24, 2016 at 12:50 | comment | added | Jason Starr | You can find such $W_i$ if $X$ admits an ample invertible sheaf. You can also find such $W_i$ if $X$ is everywhere regular. The easiest counterexample I know begins with a "nice" $X'$ that fibers over a hyperelliptic curve $C$ and such that every divisor class on $X'$ is the pullback of a divisor class on $C$. Now glue a section of the fibration to itself via the hyperelliptic involution. Remove a general point $t$ on the resulting $\mathbb{P}^1$. Let $Y$ be the fiber over one point of $C$ mapping to $t$, let $Z_1$ be the fiber over the other point of $C$. | |
| May 24, 2016 at 10:01 | history | edited | Shubhodip Mondal | CC BY-SA 3.0 |
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| May 24, 2016 at 9:51 | history | edited | Shubhodip Mondal | CC BY-SA 3.0 |
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| May 24, 2016 at 9:45 | history | asked | Shubhodip Mondal | CC BY-SA 3.0 |