Timeline for Kodaira dimension of the moduli space of curves
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2014 at 16:13 | vote | accept | Puzzled | ||
| May 10, 2014 at 16:13 | vote | accept | Puzzled | ||
| May 10, 2014 at 16:13 | |||||
| Nov 3, 2013 at 16:54 | comment | added | abx | I think this is due to Viehweg : Die Additivität der Kodaira Dimension für projektive Faserräume über Varietäten des allgemeinen Typs. J. Reine Angew. Math. 330 (1982), 132-142. | |
| Nov 3, 2013 at 16:32 | history | edited | Dan Petersen | CC BY-SA 3.0 |
deleted 73 characters in body
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| Nov 3, 2013 at 16:28 | comment | added | Puzzled | So this more general fact is true: let $f:X\rightarrow Y$ be a fibration where $Y$ and the general fiber of $f$ are of general type. Then $X$ of general type. Do you have a reference for this? | |
| Nov 3, 2013 at 16:26 | comment | added | abx | Yes. So if $\bar{M}_{g,n}$ is of general type, $\bar{M}_{g,n'}$ for $n'\geq n$ is of general type: it maps onto $\bar{M}_{g,n}$ with fibers of general type. | |
| Nov 3, 2013 at 16:24 | comment | added | Puzzled | I guess that now my question becomes this: let $f:X\rightarrow Y$ be a fibration where $Y$ and the general fiber of $f$ are of general type. Is $X$ of general type? | |
| Nov 3, 2013 at 16:13 | comment | added | Puzzled | Thank you. I see but the function $f(g)$ is just on finitely many $g$. Furthermore for any such $g$ he find an $n$ such that $\overline{M}_{g,n}$ is of general type but he does not state it for any $n\geq f(g)$. | |
| Nov 3, 2013 at 15:50 | history | answered | Dan Petersen | CC BY-SA 3.0 |