In this note, we discuss about Puiseux series and its appearance when we solve the equation . We refer to the book “Algebraic curves” of R.Walker.
Puiseux series are fractional power series:
Order of series: .
Theorem. is algebraically closed.
( – the fieldof fractional power series).
By the proof of this theorem, we can see that (an algebraic curve), we can solve (Puiseux series) such that .