Timeline for Further Questions Regarding Cohomolgoy Theory Of Sheaves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jun 16, 2012 at 13:41 | comment | added | jason mfash | Thanks again Gunnar, regarding 1- But what do you mean by $f_* \mathbb{C} $ ? It seems not suitable for the direct image sheaf case regarding 3- I know the definition of the topological Euler char of $X$. But in your previous answers, you wrote: $\chi(\mathbb{C}^{\oplus d }) = d \chi(Y) $ . How did you get this result? Thanks ! | |
| Jun 16, 2012 at 9:38 | comment | added | Gunnar Þór Magnússon | 1) I should precise that $f_*\mathbb C = \mathbb C^{\oplus d}$ only on neighborhoods of images of non-ramified points on $Y$. Here $\oplus d$ is indeed the direct sum. 2) Note that the inclusion map $f_*\mathbb C \to \mathbb C^{\oplus}$ is absolutely not canonical! You need to construct it yourself, e.g. by choosing a fine enough covering of the surface. Then the other map is simply the quotient map. 3) $\chi(X)$ is the topological Euler characteristic of $X$. For a Riemann surface of genus $g$ it is equal to $2 - 2g$ by the Riemann-Roch theorem and Hodge theory. | |
| Jun 16, 2012 at 9:02 | history | asked | jason mfash | CC BY-SA 3.0 |