Perturbing plane cruve singularities.
We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.
We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.
To a plurisubharmonic function on with logarithmic growth at infinity, we may associate the Robin functiondefined on , the hyperplane at infinity. We study the classes , and (respectively) of plurisubharmonic functions which have the form and (respectively) for which the function is not identically . We obtain an integral formula which connects the Monge-Ampère measure on the space with the Robin function on . As an application we obtain a criterion on the convergence of the Monge-Ampère...
We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.
This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.
Un résultat de positivité de théorie de Hodge nous permet de déterminer certaines pôles de la distribution pour une fonction analytique à singularité isolée. Dans le cas des courbes et des singularités quasi-homogènes on détermine l’ensemble exact des pôles. On démontre aussi que si le résidu d’une forme holomorphe est de carré intégrable sur la fibre spéciale, l’intégrale sur la fibre spéciale est limite de celle sur les fibres voisines.
On considère un polynôme , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégralesdonne des renseignements sur les racines du polynômes de Bernstein de . La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.
An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.
We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.