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On an unusual conjecture of Kontsevich and variants of Castelnuovo's lemma

J. M. Landsberg
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Abstract

Let $A=(a^i_j)$ be an orthogonal matrix with no entries zero. Let $B=(b^i_j)$ be the matrix defined by $b^i_j=\frac 1{a^i_j}$. M. Kontsevich conjectured that the rank of $B$ is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statment can be understood as a generalization of the Castelnouvo lemma and Brianchon's theorem.

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BibTeXRIS

J. M. Landsberg. 1996-07-30. On an unusual conjecture of Kontsevich and variants of Castelnuovo's lemma. https://arxiv.org/abs/alg-geom/9604023

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