When the leaves start falling, so does the plane Jacobian conjecture, or so it seems. The comparison is a bit weak in this case as two of the authors of the preprint posted today at the arXiv A Proof of the Plane Jacobian Conjecture are based in Sydney, Australia… A first glance through the paper shows that it uses Newton-polygons and the 1975 Abyankar- Moh result on embeddings of the line in the plane. Techniques that have been tried before by numerous people in their attempts to tackle the plane Jacobian conjecture (the reference to Dean in this wikipedia entry is outdated, as mentioned in an old blog entry). Still, the paper just might be correct. As there are several editors chasing me for overdue referee reports I have no time to go through the proof in detail, but if you hear more on this paper or have the energy to go through it, please leave a comment.

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Posted in rants
Written on Tue, 20 September 2005 at 5:27 pm
Tags: arxiv
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