• DOI:10.1023/A:1000697925902
• Corpus ID: 125587997

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

@article{Khoroshkin1999OnAC,
  title={On a Conjecture of Kontsevich and Variants of Castelnuovo's Lemma},
  author={Sergei Mikhailovich Khoroshkin and Dmitrii Rostislavovich Lebedev and Stanislav Pakuliak and Alexander Stolin and Valeriy N. Tolstoy},
  journal={Compositio Mathematica},
  year={1999},
  volume={115},
  pages={205-230},
  url={https://api.semanticscholar.org/CorpusID:125587997}
}

• S. Khoroshkin, D. Lebedev, +2 authors V. Tolstoy
• Published in Compositio Mathematica 1 February 1999
• Mathematics

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. 

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.