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

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

1996-04-29

arxiv.org/abs/alg-geom/9604023v2

Mathematics

Algebraic Geometry

amstex

Scientific paper

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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