Local parameter

Algebraic concept

In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than , because the local ring at a smooth point P of an algebraic curve C is always a discrete valuation ring. This valuation will show a way to count the order of rational functions having a zero or a pole at P.

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