Timeline for The degree of the Gauss map of Theta divisor
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2018 at 20:24 | comment | added | Manoel | The answer to my question is given directly in "On a theorem of Torelli". Beginning in the section you refer to "7.The branch locus of a rational map." and finishing precisely at the beginning of the next section, section 8. Thanks! | |
| Jan 7, 2018 at 23:48 | comment | added | roy smith | If I may suggest some, maybe Hartshorne II.6, Mumford *yellow book) 6.1,6.2, Shafarevich 3.1; and the paper by Andreotti on Torelli's theorem in Am.J.Math, especially for branch divisors of rational maps. | |
| Jan 7, 2018 at 23:21 | comment | added | Manoel | I'm having a bit of trouble finding a reference to read about divisors in projective varieties (since I'm very new to the subject), usually I find only for Riemann surface. So, can you give me a reference ... I need to think more about the set $U$, So, can you give me a reference ... I need to think more about the set $ U $ you use. I should not keep thinking about branch divisor of $G$, as if $G$ were a map betwenn Riemann surfaces. | |
| Jan 7, 2018 at 23:12 | vote | accept | Manoel | ||
| Jan 7, 2018 at 23:10 | comment | added | Yusuf Mustopa | Since the restriction to $G$ of $G^{-1}(U)$ is an unramified covering of $U,$ the degree of $G$ is equal to ${\#}G^{-1}(H)$ for all $H \in U.$ As a result, we only need to compute ${\#}G^{-1}(H)$ for one $H \in U$, and in the proof you describe this $H$ comes to us an element of $U \cap A.$ You should know this before calculating ${\#}G^{-1}(H)$ for this particular $H$ in order to know that it computes the degree of $G.$ | |
| Jan 7, 2018 at 23:09 | comment | added | Manoel | First, thank you for having responded. So ... I do not understand why you use the set $U=\{$ branch divisors of $G \}^c$. When you say " the same is true of $U \cap A$". I already knew from the information that the set $A$ is a dense open subset of $(\mathbb{P}^{g-1})^*$. In addition, if $U \cap A \neq \emptyset $, then $A \not\subset \{$branch points of $G\}$. And then, back to the beginning of my question .... I should know this before calculating $\#G^{-1}(H)$? | |
| Jan 7, 2018 at 4:03 | history | answered | Yusuf Mustopa | CC BY-SA 3.0 |