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On a Conjecture of Kontsevich and Variants of Castelnuovo‘s Lemma
Published online by Cambridge University Press: 04 December 2007
Abstract
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.
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