Milnor map

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Definition

Let be a complex polynomial in variables. can be viewed as a map . Let denote the zero set of . Then, on the complement of , we can define a map from to .

The Milnor map of at radius is the restriction of this map to the sphere of radius , centered at the origin, to .

Facts=

By the Milnor fibration theorem, the Milnor map is a fibration whenever the origin is an isolated singular point of . Under such circumstances, it is termed the Milnor fibration.