Timeline for Writing down minimal Weierstrass equations
Current License: CC BY-SA 2.5
5 events
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| Dec 8, 2010 at 20:34 | comment | added | Pete L. Clark | At the request of a colleague: if anyone is in doubt that Liu's characterization of Liu's algorithm as not being based on Namikawa-Ueno is more accurate than my own...please don't be. I apologize for the mistake. | |
| Jan 26, 2010 at 0:04 | comment | added | Qing Liu | Yes there exists an algorithm for curves of genus 2 computing the reduction of the minimal regular model except over 2. The computer program in the SAGE package. The output of the program give the reduction type classified by Namikawa-Ueno, by the it is not based on it. The program also gives other invariants as the conductor of the Jacobian and the (geometric) component group of the Néron model of the Jacobian. These invariants are given by formulas depending only on the reduction type as in the elliptic case (except in a very special case, no more space left for comments...). | |
| Jan 4, 2010 at 1:47 | comment | added | JSE | In the acknowledgments he says that paper was his thesis, so I think I just misremembered what it was about! | |
| Jan 4, 2010 at 0:54 | comment | added | Pete L. Clark | I didn't know that Szydlo worked on the case of 2-dimensional local fields. His published work -- see math.uga.edu/~pete/Szydlo.pdf -- treats the case of an elliptic curve over a DVR with imperfect residue field. I wonder if he has any plans to make the rest of his thesis available? In genus 2, Liu's algorithm is based on the work of Namikawa and Ueno. The classification in higher genus involves combinatorics which quickly get out of hand. | |
| Jan 3, 2010 at 23:52 | history | answered | JSE | CC BY-SA 2.5 |