Topology of polar weighted homogeneous hypersurfaces

Abstract

Polar weighted homogeneous polynomials are the class of special polynomials of real variables $x_i,y_i,i=1,...,n$ with $z_i=x_i+\sqrt{-1}{y}_i$, which enjoys a "polar action". In many aspects, their behavior looks like that of complex weighted homogeneous polynomials. We study basic properties of hypersurfaces which are defined by polar weighted homogeneous polynomials.

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