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

Published online by Cambridge University Press:  04 December 2007

J.M. LANDSBERG
J.M. LANDSBERG
Affiliation:
Laboratoire de Mathématiques, Université Paul Sabatier, UFR-MTG 31062 Toulouse Cedex4, France; e-mail: jml@picard.ups-Hse.fr
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Abstract

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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.

Keywords

rational curvesCremona transformquadricsCastelnuovo‘s lemmaBrianchon‘s theoremGale transformassociation.
Type
Research Article
Information
Compositio Mathematica , Volume 115 , Issue 2 , February 1999 , pp. 205 - 230
Copyright
© 1999 Kluwer Academic Publishers