Timeline for Moduli space of curves over $\mathbb Z$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6, 2011 at 9:35 | comment | added | Thomas Riepe | Parts of a preliminary version of vol. II of "Geometry of algebraic curves" seem to be still online: isites.harvard.edu/fs/docs/icb.topic471314.files/gacIIframe.pdf | |
| May 27, 2011 at 12:43 | comment | added | naf | I don't know any reference which explains all the machinery. Another good reference is Gieseker's "Lectures on moduli of curves" which gives a fairly complete algebraic construction of the moduli of stable curves using GIT. | |
| May 25, 2011 at 15:49 | comment | added | HNuer | @ulrich: I have Mumford's GIT, but does he actually include the details there? In the famous paper of DM, already on the first page they start quoting details from Hartshorne's Duality and Residues, which I haven't studied. I was hoping for something more beginner friendly, which included the details of why the relative dualizing sheaf is ample and in fact why is exists/what it is. I know now how to describe it explicitly but only after piecing together many different sources. Is there anything which actually explains the machinery necessary? | |
| May 25, 2011 at 12:45 | answer | added | Dan Petersen | timeline score: 5 | |
| May 25, 2011 at 12:38 | comment | added | naf | The coarse moduli space over $\mathbb{Z}$ is constructed in Mumford's Geometric Invariant Theory. An easier to read reference might be the article by Mumford: Stability of projective varieties. Enseignement Math. (2) 23 (1977), no. 1-2, 39–110. As a stack, it is constructed in the paper of Deligne and Mumford "The irreducibility of the space of curves of a given genus". In fact, they construct the moduli stack of stable curves over $\mathbb{Z}$. | |
| May 25, 2011 at 9:03 | comment | added | quim | a link to the book: springerlink.com/content/… | |
| May 25, 2011 at 8:24 | comment | added | Kevin H. Lin | OMG! Volume II of "Geometry of Algebraic Curves"?! I'm so happy that it's finally coming out -- I had actually given up all hope that it would ever happen. | |
| May 25, 2011 at 8:12 | history | asked | HNuer | CC BY-SA 3.0 |