Timeline for Computationally bounding a curve's genus from below?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2010 at 7:08 | vote | accept | Dror Speiser | ||
| Apr 1, 2010 at 15:06 | comment | added | damiano | Agreed, though the "purging out of roots" might require computing the gcd several times. Also, you should make sure to begin with that the curve is geometrically integral, since otherwise the bound you get is off by the number of geometric irreducible components of C. Note also that you really only get a lower bound if you do not deal with the singular points of C. | |
| Apr 1, 2010 at 13:34 | comment | added | Dror Speiser | It doesn't seem you need to factor polynomials. Finding the number of distinct roots is done by dividing by the gcd with the derivative. The degrees of the resultants are $O(d^2)$, making the computation in the rationals slow. Of course, as is mentioned above, one can reduce modulo. Finally, all of this needs to be implemented for sage (computation of genus for curve with integer/rational coefficients). | |
| Apr 1, 2010 at 11:45 | history | edited | damiano | CC BY-SA 2.5 |
expanded, given the request in a later question!
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| Mar 31, 2010 at 9:50 | history | edited | damiano | CC BY-SA 2.5 |
added 2 characters in body
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| Mar 31, 2010 at 9:37 | history | answered | damiano | CC BY-SA 2.5 |