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2 results

  • Corrigendum: on a conjecture of Kontsevich and variants of Castelnuovo's lemma

  • J. M. Landsberg
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 4 / July 2004
    Published online by Cambridge University Press:
    04 December 2007, p. 1112
    Print publication:
    July 2004
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  • In the Mathematical Review of ‘On a conjecture of Kontsevich and variants of Castelnuovo's lemma’ [Compositio Mathematica 115 (1999), 205–230], Gizatullin pointed out that the proof as written is incomplete for the complex case because the possibility of a certain equation vanishing identically was ignored. This corrigendum addresses the missing case. Note that it is simply another iteration of the argument already present in the article.

  • On a Conjecture of Kontsevich and Variants of Castelnuovo‘s Lemma

  • J.M. LANDSBERG
  • Journal:
    Compositio Mathematica / Volume 115 / Issue 2 / February 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 205-230
    Print publication:
    February 1999
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  • Let A=(aij) be an orthogonal matrix (over R or C) with no entries zero. Let B= (bij) be the matrix defined by bij= 1/ai j. M. Kontsevich conjectured that the rank of B is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statement can be understood as variants of the Castelnuovo lemma and Brianchon‘s theorem.