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Perturbing plane cruve singularities.

Eduardo Casas-Alvero, Rosa Peraire (2003)

Revista Matemática Iberoamericana

We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.

Plurisubharmonic functions with logarithmic singularities

E. Bedford, B. A. Taylor (1988)

Annales de l'institut Fourier

To a plurisubharmonic function u on C n with logarithmic growth at infinity, we may associate the Robin function ρ u ( z ) = lim sup λ u ( λ z ) - log ( λ z ) defined on P n - 1 , the hyperplane at infinity. We study the classes L + , and (respectively) L p of plurisubharmonic functions which have the form u = log ( 1 + | z | ) + O ( 1 ) and (respectively) for which the function ρ u is not identically - . We obtain an integral formula which connects the Monge-Ampère measure on the space C n with the Robin function on P n - 1 . As an application we obtain a criterion on the convergence of the Monge-Ampère...

Puiseux Expansion of a Cuspidal Singularity

Maciej Borodzik (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.

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