Timeline for Higher dimensional version of the Hurwitz formula?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2021 at 11:55 | comment | added | user122276 | PS: I have a question to other users of the forum: As you may verify yourself: Stefan Kohl is not doing algebraic geometry and knows nothing about the subject. Still he deletes posts that are outside of his expertise, posts that may be helpful for other users on the forum. Do you want someone like this to be a "moderator " on this forum? | |
| Jul 25, 2021 at 10:44 | comment | added | user122276 | This is proved in Fulton, "Intersection Theory", Ex.18.3.9). Since $f$ is etale, there is no "ramification locus" $R(f) \subseteq Y$ as there is in the "Hurwitz formula" for curves. A more general formula would be a formula relating $p_a(X), p_a(Y)$ and $R(f)$ for any finite map $f$. | |
| Jul 25, 2021 at 10:44 | comment | added | user122276 | Question: "In Hartshorne IV.2, notions related to ramification and branching are introduced, but only for curves. The main result is the Hurwitz formula." $$\text{ }$$ Answer: This answer was deleted by Stefan Kohl, still it may have interest for you. There is an etale version of the Hurwitz formula. If $f: X^n \rightarrow Y^n$ is a finite etale map of projective schemes of dimension $n$ over a field $k$, there is the following formula (an "etale Hurwitz formula"): $$Et.\text{ }p_a(X)=deg(f)p_a(Y)+(-1)^n(deg(f)-1).$$ | |
| Jul 24, 2021 at 13:31 | review | Suggested edits | |||
| Jul 24, 2021 at 15:02 | |||||
| Dec 25, 2015 at 19:40 | answer | added | Lucas Braune | timeline score: 13 | |
| Mar 20, 2013 at 19:36 | comment | added | rfauffar | well, technically you can define the degree of a divisor with respect to a fixed ample divisor... | |
| Jan 11, 2013 at 1:05 | answer | added | Sándor Kovács | timeline score: 34 | |
| Jan 9, 2012 at 15:58 | answer | added | Liviu Nicolaescu | timeline score: 5 | |
| Aug 3, 2011 at 17:29 | vote | accept | Jesko Hüttenhain | ||
| Aug 3, 2011 at 3:42 | answer | added | Jack Huizenga | timeline score: 19 | |
| Aug 3, 2011 at 3:15 | answer | added | Christian Liedtke | timeline score: 29 | |
| Aug 3, 2011 at 2:51 | comment | added | Mohammad Farajzadeh-Tehrani | degree of a divisor is only defined over curves. | |
| Aug 3, 2011 at 1:53 | history | asked | Jesko Hüttenhain | CC BY-SA 3.0 |