24 research outputs found
On the approximate jacobian Newton diagrams of an irreducible plane curve
We introduce the notion of an approximate jacobian Newton diagram which is
the jacobian Newton diagram of the morphism , where is a
branch and is a characteristic approximate root of . We prove that
the set of all approximate jacobian Newton diagrams is a complete topological
invariant. This generalizes theorems of Merle and Ephraim about the
decomposition of the polar curve of a branch
Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility
In this paper we characterize, in two different ways, the Newton polygons
which are jacobian Newton polygons of a branch. These characterizations give in
particular combinatorial criteria of irreducibility for complex series in two
variables and necessary conditions which a complex curve has to satisfy in
order to be the discriminant of a complex plane branch