Timeline for projective map from $\overline{\mathcal{M}}_{0,n}$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2015 at 14:10 | comment | added | Hacon | I see. The only results of this kind that I know are from the MMP. If you contract a codim \geq 2 subset you get something not Q-factorial; if you contract a K_X+D negative extremal ray via f:X->Y (where (X,D) is klt) then (Y,f_*(D+H)) is klt where H is an appropriate ample divisor on X. Unluckily, I suspect that this is not what you are after.... | |
| Feb 3, 2015 at 10:52 | history | edited | IMeasy | CC BY-SA 3.0 |
(made the question clearer and added the hypothesis of normality)
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| Feb 3, 2015 at 10:50 | comment | added | IMeasy | @Hacon: yes you are right, it was probably me who expressed badly the question. I will re-edit eventually. My point is that I am not that good enough at birational geometry to understand what kind of singularity will I get just by knowing the set of exceptional curves (or divisors, if you prefer). | |
| Feb 3, 2015 at 0:24 | comment | added | Hacon | Suppose that $f:X\to Y$ is a birational morphism of normal projective varieties, then doesn't $X$ and the set of exceptional curves determine $Y$? (i.e. given $f':X\to Y'$ birational of normal varieties with the same set of exceptional curves, then $f'=f$. Maybe I misunderstood the question?) | |
| Feb 2, 2015 at 14:56 | comment | added | IMeasy | @Jason: and would normality be enough, in your opinion? | |
| Jan 31, 2015 at 21:38 | comment | added | Jason Starr | At the very least, you will need to specify that the image of $f$ is normal. Otherwise, you cannot specify the image uniquely just by knowing the pullback of the ample cone (which, I suspect, is what you are getting at via the contracted $F$-curves). | |
| Jan 31, 2015 at 18:04 | comment | added | Francesco Polizzi | In general the knowledge of the dual graph of the singularity does not identify its analytic type. When this happens, the singularity is called "taut". Taut two-dimensional singularities were classified by Laufer, see Math. Ann.205 (for instance, quotient singularities are taut). I do not know whether there are similar results in higher dimension. | |
| Jan 31, 2015 at 17:55 | history | asked | IMeasy | CC BY-SA 3.0 |