Timeline for Moving a Weil divisor on a normal surface away from a finite set of closed points
Current License: CC BY-SA 3.0
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| Jul 31, 2011 at 17:16 | comment | added | Francesco Polizzi | On a smooth surface the answer is certainly yes, since any divisor is lineraly equivalent to the difference of two very ample divisors. Of course, the divisor $E$ lineraly equivalent to $D$ and avoiding $X$ will not be effective in general. But the OP does not require effectiveness. In your example, it is sufficient to take $E=L-F$, where $L$ is the strict transform of a general line and $F$ the strict transform of a line passing to the point you are blowing up. | |
| Jul 31, 2011 at 17:10 | vote | accept | Ariyan Javanpeykar | ||
| Jul 31, 2011 at 17:05 | history | answered | J.C. Ottem | CC BY-SA 3.0 |