On a conjecture of Kontsevich and variants of Castelnuovo's lemma Academic Article uri icon


  • 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/aij. 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.

author list (cited authors)

  • Landsberg, J. M.

publication date

  • January 1999