On the Roots of an Extended Lens Equation and an Application

  • Mutsuo OkaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


We consider zero points of a generalized Lens equation \(L(z,{\bar{z}})={\bar{z}}^m-{p(z)}/{q(z)} \) and also harmonically splitting Lens type equation \(L^{hs}(z,{\bar{z}})=r({\bar{z}})-p(z)/q(z)\) with \(\deg \, q(z)=n,\,\deg \,p(z)\le n\) whose numerator is a mixed polynomials, say \(f(z,{\bar{z}})\), of degree \((n+m; n,m)\). To such a polynomial, we associate a strongly mixed weighted homogeneous polynomial \(F(\mathbf{z},{\bar{\mathbf{z}}})\) of two variables and we show the topology of Milnor fibration of F is described by the number of roots of \(f(z,{\bar{z}})=0\).


Lens equation Mixed curves Link components 

2000 Mathematics Subject Classification

14P05 14N99 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTokyo University of ScienceShinjuku-ku, TokyoJapan

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