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1 results

  • On a Jacobian Identity Associated with Real Hyperplane Arrangements

  • Kazuhiko Aomoto, Peter J. Forrester
  • Journal:
    Compositio Mathematica / Volume 121 / Issue 3 / May 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 263-295
    Print publication:
    May 2000
    • Article
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  • For $x\in (a_{j-1}, a_j)\ (j=1,\ldots, p+1;\ a_0\!:=-\infty, \ a_{p+1} \!:=\infty)$ the mapping $T_j\!: w=x-\sum ^p_{l=1}\lambda _l/(x-a_l)\ (\lambda _l$>$0, \ a_l\in$R) is onto R. It was shown by G. Boole in the 1850's that $\sum ^{p+1} _{j=1}[(\partial w/\partial x) ^{-1}] _{x=T^{-1}_j(w)}=1.$ We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.