Detecting asymptotic non-regular values by polar curves

Abstract

We locate the Malgrange non-regular values of a given polynomial function $f:\bC^n \to \bC$ by using a series of affine polar curves. We moreover show that all non-trivial Malgrange non-regular values of $f$ are indicated by a single "super-polar curve" which we introduce here, providing also an effective algorithm of detection.