=ADD=
=reftype=
14
=number=
00-10
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2000/00-10.ps.gz
=year=
2000
=month=
04
=author=
Stadelmeyer; Peter
=title=
Algebraic Extensions in the Resolution of Curve-Singularities
=abstract=
Let $\acurveC$ be an irreducible algebraic curve in the affine
plane and let $\cbranch$ be a curve-branch of $\curveC$.
In this paper we compare the algebraic extensions 
necessary to resolve $\cbranch$ either by quadratic
transformations or Puiseux-series expansions. 
    
It is well known that the residual field of $\cbranch$ is 
isomorphic to the coefficient field of a rational
Puiseux-expansion of $\cbranch$. 
We will show, that this is also true for the coefficient field
of quadratic transformations of $\cbranch$. This allows us
to give an a-priory bound for the degree of the field extension
necessary to resolve $\cbranch$.
    
We will also present an alternative definition of 
rational Puiseux-expansions based on the implicit
function theorem and quadratic transformations.
=sponsor=
FWF project number P11160-TEC ``HySaX''
=keywords=
algebraic geometry, plane curves, algebraic extensions, resolution,
Puiseux series, quadratic transformations, singularities