On a Jacobian Identity Associated with Real Hyperplane Arrangements

Wiley - Tập 121 - Trang 263-295 - 2000
Kazuhiko Aomoto1, Peter J. Forrester2
1Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya
2Department of Mathematics, University of Melbourne, Parkville, Australia

Tóm tắt

For $$x \in (a_{j - 1} ,a_j )(j = ,...,p + 1;a_0 : = - \infty ,a_{p + 1} : = \infty )$$ the mapping $$T_j :w = x - \sum {_{l = 1}^p {\lambda }_l /(x - a_l )({\lambda }_l >0,a_l } \in {R)}$$ is onto R. It was shown by G. Boole in the 1850's that $$\sum {_{j = 1}^{p + 1} } [(\partial w/\partial x)^{ - 1} ]_{x = T_j^{ - 1} (w)} = 1$$ We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.

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Wiley

Tập 121

263-295

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