Timeline for A family of examples of (Brody) hyperbolic surfaces
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2014 at 17:41 | comment | added | Jason Starr | @Mehdi: "You mean the Zariski open ..." Yes, indeed. Thank you for catching the typo -- it is now corrected. | |
| Mar 31, 2014 at 17:41 | history | edited | Jason Starr | CC BY-SA 3.0 |
Changed D(y) to D(z)
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| Mar 31, 2014 at 17:16 | comment | added | Mehdi | Jason, you mean the Zariski open subset $D(zw)$? | |
| Mar 31, 2014 at 13:55 | comment | added | Mehdi | This is a way of thinking about this problem: we can define the map $S \righarrow \mathbb{P}^1$ by $(x, y, z, w) \mapsto (x, y)$ which is defined everywhere except the finite set $\Sigma$ of the singularities of the surface $S$. This set can be blown up to yield a holomorphic map from the blowup of $S$, i.e. $g: \overline{S} \rightarrow \mathbb{P}^1$. Now if we could prove that the map $g$ can be factorized as $\overline{S} \rightarrow C \rightarrow \mathbb{P}^1$ where $C$ is a hyper elliptic curve, then we can almost prove the hyperbolicity of the surface $S$ by a standard argument. | |
| Mar 31, 2014 at 13:54 | history | edited | Jason Starr | CC BY-SA 3.0 |
added 307 characters in body
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| Mar 31, 2014 at 13:47 | comment | added | Mehdi | Yes, Jason, I ask about the hyperbolicity of the affine surface where $zw$ is nonzero. | |
| Mar 31, 2014 at 13:34 | comment | added | Jason Starr | Just to clarify, are you amending your question to ask about hyperbolicity of the affine surface where $zw$ is nonzero? | |
| Mar 31, 2014 at 13:29 | comment | added | Mehdi | I guess that these are all kinds of rational curves in the surface $S$, it means that there is no rational/elliptic curve in the part $\{z\neq 0 \}\cup \{w\neq0\}$. | |
| S Mar 31, 2014 at 11:18 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Mar 31, 2014 at 11:18 | history | made wiki | Post Made Community Wiki by Jason Starr |