Talk:Jacobian conjecture

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Firstly, on the conjecture. The stronger form is that F can be inverted by polynomials: i.e. that F gives a ring automorphism of the polynomial ring. Is this known to be equivalent.

Secondly on Carolyn Dean: what I know from the Web:

- she wrote a PhD supervised by Lance Small at University of California San Diego in 1986

- she is now a lecturer at the University of Michigan

- she will be presenting the proof at talks starting December 2.

On the proof, Melvin Hochster is now vouching that it is correct. It depends on some earlier results in the field.


A few days ago I posted here that I thought the proof for n = 2 by Carolyn Dean had been withdrawn, and stated that I was in the process of verifying this.

Today (1/1/06) I have received an e-mail from Melvin Hochster confirming that, indeed, the proof was retracted soon after it was announced (aforesaid talks on Dec. 2, 2004 never took place), and that Carolyn Dean is still trying to repair the flaw in her proof.

So for the time being it would be best to remove this phrase in the article:

<< The Jacobian conjecture has been proved for polynomials of degree 2,

Sincerely,

Dan AsimovDaqu 19:20, 1 January 2006 (UTC)

But that is degree d = 2, not number of variables N. Charles Matthews 21:27, 1 January 2006 (UTC)

Thanks for pointing out my silly confusion, Charles. I was influenced by the statement at top of this page, which perhaps should be a) dated and b) updated.

4.239.30.27 02:03, 2 January 2006 (UTC)

There seems to be a feeling that for large N the conjecture may turn out to be false.

Charles Matthews 15:11, 21 Nov 2004 (UTC)

Two web references for the story:

[edit] origin of name

Moh's webpage, listed in the external links, explains he gave the conjecture this name. What's the reference for Abhyankar naming it? --C S (Talk) 06:08, 4 February 2007 (UTC)