According to the retraction notice, published in the July 2017 issue of Manuscripta Mathematica, the author Ilya Karzhemanov “has not admitted to the alleged errors and disagrees with the retraction.”
It’s unclear when exactly the paper was retracted, but Karzhemanov, now associate professor at the Moscow Institute of Physics and Technology, posted the now-retracted paper on arXiv in June 2017 and explained his “strong disagreement” with the retraction:
The present situation around my paper is a result of personal conflict and is a part of continuous manhunt on me (initiated unfortunately by my former advisor Cheltsov).
We asked Karzhemanov about the personal conflict, but he said he did not want to discuss “personal matters.”
Ivan Cheltsov, who supervised Karzhemanov’s PhD from 2007 to 2010, told us “there is no conflict.” Cheltsov, a professor of mathematics at the University of Edinburgh, explained that he did not write to Manuscripta Mathematica about Karzhemanov’s now-retracted paper but said “it was absolutely clear that there is a problem with this paper:”
I emailed people working on these types of problem and informed them about this paper… I asked them to check the proof. And I emailed Ilya as well so that he knows what I am doing.
Karzhemanov argued that aside from “one or two small misprints,” which he says he corrected in the arXiv version, his paper is correct. He told us that he sent the journal explanations defending his work (1, 2), but “the evidence in its favor were completely ignored.”
The article Some pathologies of Fano manifolds in positive characteristic by Ilya Karzhemanov published under DOI:10.1007/s00229-015-0796-9 has been retracted by the journal’s editorial board.
The retraction has been made because in a post-publication peer review process it was reported by three independent reviewers that the paper contains errors which invalidate its main results.
All three reviewers presented examples which show that Proposition 2.9 and Lemma 2.12 are wrong. Furthermore it was pointed out that the way the Fano variety X in the Main Theorem 1.4 is constructed is in contradiction with the Theorem of Campana and Kollar-Miyaoka-Mori that every smooth Fano variety over an algebraically closed field is chain connected.
The author of the paper has not admitted to the alleged errors and disagrees with the retraction.
The online version of this article contains the full text of the retracted article as electronic supplementary material.
The retraction notice, though not the paper, has been indexed by Clarivate Analytics’ Web of Science, which we typically use to determine how often a paper has been cited. We asked the editor for more details but he referred us to the notice.
Other problematic papers?
Cheltsov elaborated on the personal situation Karzhemanov referenced in his arXiv post. Cheltsov told us that a few years go several mathematicians informed him that Karzhemanov had written some problematic papers. Cheltsov says he checked a few of Karzhemanov’s papers and discussed them with him to help resolve any issues.
Karzhemanov, however, says that the discussion about the quality of his work occurred behind his back and has affected his career. “It was impossible for me to argue” with the criticism, he says.
Cheltsov explained that he believes Karzhemanov considered these efforts to discuss the papers and correct any inaccuracies “a personal offense.”
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