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Topic: Jacobian problem in dimension 2 solved
Replies: 10   Last Post: Dec 22, 2005 10:48 PM

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Lee Rudolph

Posts: 3,143
Registered: 12/3/04
Re: Jacobian problem in dimension 2 solved
Posted: Dec 12, 2005 7:49 AM
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David C. Ullrich <ullrich@math.okstate.edu> writes:

>On 12 Dec 2005 06:19:36 -0500, lrudolph@panix.com (Lee Rudolph) wrote:
>

>>marcfrisch@hotmail.com writes:
>>

>>>Hello,
>>>Joel Briancon (University of Nice, France) has solved the Jacobian
>>>problem in dimension 2:
>>>Let f,g be two polynomials in C[x,y] such that the Jacobian determinant
>>>is a nonzero complex number. We prove that the polynomial map
>>>(f,g):C2-->C2 is an algebraic automorphism.
>>>
>>>You can find the proof at
>>>http://arxiv.org/abs/math.AG/0512174
>>>
>>>Best regards,
>>>Marc

>>
>>Is there overmuch reason to believe this latest announced
>>proof, given the amazing record of the Jacobian problem
>>for eliciting bogus proofs from mathematicians of considerable
>>ability and reputation (as well as others, naturally)? Has,
>>for instance, anyone else with relevant expertise endorsed it
>>yet?

>
>I wouldn't know about the history of the problem, but
>it seems to me that they couldn't post it on the internet
>if it wasn't right. Or at least they wouldn't.


Heh. Heheheh.

http://arxiv.org/abs/math.AG/0509431
http://arxiv.org/abs/math.AC/0407332
http://arxiv.org/abs/math.AC/0406613
http://arxiv.org/abs/math.AG/9912196
http://groups.google.com/group/sci.math.research/msg/b5367bac8133ab98?

Lee Rudolph





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