Timeline for Upper bound on greatest prime of bad reduction for a plane curve
Current License: CC BY-SA 2.5
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| Apr 1, 2010 at 9:06 | comment | added | Dror Speiser | @Damiano: that sounds very good and that it can reduce the exponent of $d$ in the final algorithm. But, I don't understand this explicitly. Especially the "find an open subset $U$". Can you explain this and the Hurwitz stuff in a longer and computationally explicit answer? | |
| Apr 1, 2010 at 7:29 | comment | added | damiano | This seems correct. Roughly, what I had in mind was that you look at the singular subscheme S of your curve over Z, find an open subset U of Spec(Z) where S is smooth (assuming for simplicity that S is reduced), and then choose any prime from U to do your computation. Let me also iterate that I really think that it is far more practical to use the Hurwitz formula: you reduce most of your computations to computing resultants and gcd's of polynomials of degree at most d to get an "approximate" bound and throw in some integral closures to finish off, if needed. | |
| Mar 31, 2010 at 23:14 | history | answered | Dror Speiser | CC BY-SA 2.5 |