Topology of polar weighted homogeneous hypersurfaces

Abstract

Polar weighted homogeneous polynomials are special polynomials of real variables x_i, y_i, i = 1, ..., n with z_i = x_i + $¥sqrt{-1}$y_i which enjoy 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.