Algebroid Curves in Positive Characteristic
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813 Antonio Campiilo
Algebroid Curves in Positive Characteristic
Springer-Verlag Berlin Heidelberg New York 1980
Author Antonio Campillo Departamento de Algebra y Fundamentos, Facultad de Ciencias, Universidad de Valladolid Valladolid/Spain
AMS Subject Classifications (1980): 14 B05, 14 H 20 ISBN 3-540-10022-9 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-10022-9 Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by SpringeroVerlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
INTRODUCTION
A since
number
Zariski
(the of
are
over
equivalent
that
more
recently
of
the
in
any
field
which
attempt
is
the
being
r a
chain
an of
algebroid
arbitrary
of
an
case and
( 18 ) , a n d
curves
characteristic, instead in
Salamanticiensis any
irreducible
longer.
first
as
main
appeared
algebraic in
curves
a work
(Universidad Essentially
algebroid
an
zero.
expansion
completely
over
the
Puiseux
characteristic
plane
of
using
o.f t h e
developed
was
available
the
development
It
it
curve
[]
by
G.
de is
based
on
= k({x,y~]
type
=
x(z
y = y(z
z
a systematic
of
x
by
give
parametrizations
not
zero
3 ) .
employed
Acta
algebroid
attention
Moh
obtain
and
of
( 15)9
to
in
plane
extensive
Hamburger-Noether
a parametrization k
received
,
Those
However
called
published
appeared
characteristic
so
characteristic.
Salamanca)
of
of
initially).
expansion
usually
case
field
irreducible
of
have
Equisingularity"
Lejeune
to
Hamburger-Noether
Ancochea,
over
not
[
of
closed
in
particular
available"
equisingularity
The an
has
intend
expansion
as
are
equisingularity
considered
notes
algebraically tool
the
closed
AngermBIler
These theory
in
p > 0
papers
of
"Studies
Zariski
characteristic a few
his
a-n a l g e b r a i c a l l y
situation
only
definitions
published
definitions curves
of
element relations
of
r r
the
)
)
,
quotient
field
of
[]
,
obtained
from
x~y
IV
y
=
a0t
x +
2
aO2x
+
. . .
+
2 x
=
Zr_1 where
a.. jl
C
a plane
Puiseux
expansion
and
are
determined
the
curve,
by
the
singularities
the
of
I
well
contains
an
over
introduce
an
the
between given
the by
the
of
that
for
derived
the
local
from
ring,
etc...
and
results
of
on
resolution
Chapter
comparison
I I
of
is
of it w i t h
devoted
the
zero. a complex
ones, and
of t h e maximal iV. and
of
From compute
Newton
exponents
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