Timeline for Image of a hypersurface under a map $\mathbb CP^n\to \mathbb CP^n$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 14 at 6:30 | comment | added | LAPRAS | I think that is not correct. Probably only we can say that $f_*H \in \mathcal{O}(d^{n-1}m)$, as a divisor. For example, consider the map $f: \mathbb{P}^n \to \mathbb{P}^n$ defined by $(x_0, x_1, ...x_n) \to (x_0^m, x_1^m, ...x_n^m)$, then the image of the hyperplane defined by $x_i=0$ is itself. | |
| Feb 26, 2014 at 8:23 | comment | added | aglearner | Jason, thank you for this comment, you are right of course. | |
| Feb 26, 2014 at 8:22 | history | edited | aglearner | CC BY-SA 3.0 |
added 12 characters in body
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| Feb 26, 2014 at 3:53 | comment | added | Jason Starr | The degree of the Cartier divisor $\phi_*H$ is $d^{n-1}m$, not $dm$. You can compute it explicitly using norms. You can read about this in the section of Mumford's, "Lectures on Curves on an Algebraic Surface" that discusses norms and pushforwards of effective Cartier divisors. There may also be a discussion in the appendix of Fulton's "Intersection Theory" using Herbrand quotients (need to check that one). | |
| Feb 25, 2014 at 22:54 | answer | added | Francesco Polizzi | timeline score: 3 | |
| Feb 25, 2014 at 22:09 | comment | added | Alex Degtyarev | I think this is (part of) what is called elimination theory: you spell everything out and eliminate the old coordinates. In principle, this is algorithmical, but, as far as I understand, absolutely unpractical. | |
| Feb 25, 2014 at 21:55 | history | edited | agt | CC BY-SA 3.0 |
edited title
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| Feb 25, 2014 at 21:52 | history | asked | aglearner | CC BY-SA 3.0 |