Timeline for Number of $(-1)$ curves on toric surfaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 15, 2011 at 21:45 | comment | added | Dustin Cartwright | MP, you're correct that if you blow-up a point on a (-1)-curve, the strict transform of the curve has self-intersection -2. Nonetheless, you can have arbitrarily many (-1)-curves on a toric variety. First, by blowing up repeatedly, you can get arbitrarily many torus fixed points. Second, blow up these fixed points, each of which will yield a (-1)-curve. | |
| Aug 15, 2011 at 11:46 | comment | added | naf | Blowing up a torus invariant point creates two new torus invariant points on the exceptional curve! | |
| Aug 15, 2011 at 11:43 | comment | added | M P | I was thinking of the blow up of the plane at 3 points: I thought that you could only blow up torus invariant points that this introduced new exceptional curves at the expense of changing the previous exceptional to $(-2)$-curves or worse... I guess I was wrong! | |
| Aug 15, 2011 at 11:21 | comment | added | naf | Yes. What is special about 6? | |
| Aug 15, 2011 at 10:53 | comment | added | M P | In fact, can a toric surface have more than 6 exceptional curves? | |
| Aug 15, 2011 at 10:27 | history | answered | naf | CC BY-SA 3.0 |