Timeline for Hn(X, OX) = 0 for X birational to a regular affine variety?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 13, 2013 at 15:02 | vote | accept | anonymous | ||
| Aug 13, 2013 at 15:02 | history | edited | anonymous | CC BY-SA 3.0 |
missing (implicit) hypotheses
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| Aug 13, 2013 at 3:58 | answer | added | Karl Schwede | timeline score: 4 | |
| Aug 12, 2013 at 22:29 | answer | added | Olivier Benoist | timeline score: 8 | |
| Aug 12, 2013 at 20:29 | comment | added | Piotr Achinger | As stated this is not true: take $X=\mathbb{A}^2$, $Y = X\setminus (0, 0)$ and $f:Y\to X$ the inclusion. Then $H^1(Y, \mathcal{O}_Y) \neq 0$. Maybe assume $f$ proper? | |
| Aug 12, 2013 at 18:53 | comment | added | meh | @Jason- You are correct. If that is what he is asking, my argument won't do | |
| Aug 12, 2013 at 17:50 | comment | added | Jason Starr | @aginensky: I believe what you are saying is correct, but I think that is a little different from what the OP asks. In your comment, I believe that $n$ equals the dimension of $X$ (and $Y$). However, I do not see anywhere that the OP specifies that $n$ should be the dimension -- I think the OP wants the result for all $n>0$. | |
| Aug 12, 2013 at 16:12 | comment | added | meh | Am I missing something ? Let $F$ be arbitrary coherant sheaf. The $R^if_{*}(F)$ are quasi coherant so all their higher cohomology (on $X$) vanishes too. Hence the Leray SS degenerates and then your claim follows (for any $F$) since it is supported in dimension $= n-1$ and so standard base change shows $R^n f_{*}(F)$ vanishes | |
| Aug 12, 2013 at 15:53 | review | First posts | |||
| Aug 12, 2013 at 15:57 | |||||
| Aug 12, 2013 at 15:36 | history | asked | anonymous | CC BY-SA 3.0 |