Timeline for resolution of singular points on curve
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2011 at 0:59 | comment | added | Karl Schwede | Just a quick comment, the algebra quim describes is called the Rees algebra. It might help you find references where some examples are worked out. | |
| May 31, 2011 at 16:15 | comment | added | quim | The rough idea is as follows (though I recommend to get a real explanation in full, if someone can give a better reference). Let ${\mathfrak p}\subset R$ be the ideal of the scheme at which you want to blow up (I assume R=k[x,y]). Let A be the graded algebra $\bigoplus {\mathfrak p}^n$. Then the blowup is a variety, projective over R, associated to the graded algebra A. To obtain its equations in $\mathbb{P}^n_R$, you need to know a minimal set of generators (n+1 of them) and their relations. | |
| May 31, 2011 at 16:08 | comment | added | quim | Hartshorne explains the general construction via the (sheaf of) graded algebras associated to a (sheaf of) ideals in II.7. There must be a simpler exposition for the affine case written somewhere (to avoid the formalism of sheaves), but unfortunately I don't know a reference. :( Sorry! | |
| May 31, 2011 at 15:12 | comment | added | user565739 | Could you say more about "blowup centered at that scheme" or give a reference for this? Because I learned blow up by Fulton's book, which is blowing-up at (closed and rational) points only. Thanks. | |
| May 31, 2011 at 15:05 | history | answered | quim | CC BY-SA 3.0 |