Local parameter
In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is just a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than (or even schemes), because the local ring at a smooth point P of an algebraic curve C (defined over an algebraically closed field) is always a discrete valuation ring. This valuation will endow us with a way to count the order (at the point P) of rational functions (which are natural generalizations for meromorphic functions in the non-complex realm) having a zero or a pole at P.
Wikipage redirect
Link from a Wikipage to another Wikipage
primaryTopic
Local parameter
In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is just a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than (or even schemes), because the local ring at a smooth point P of an algebraic curve C (defined over an algebraically closed field) is always a discrete valuation ring. This valuation will endow us with a way to count the order (at the point P) of rational functions (which are natural generalizations for meromorphic functions in the non-complex realm) having a zero or a pole at P.
has abstract
In the geometry of complex alg ...... multiplicities in a local way.
@en
Wikipage page ID
21,309,351
page length (characters) of wiki page
Wikipage revision ID
532,093,416
Link from a Wikipage to another Wikipage
comment
In the geometry of complex alg ...... having a zero or a pole at P.
@en
label
Local parameter
@en