On the δ = const deformations/degenerations of singularities of complex plane curves.
نویسنده
چکیده
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total δ invariant is preserved (aka equi-generic deformations). We restrict primarily to the deformations of singularities with smooth branches. A new invariant of the singular type is introduced: the dual graph. It imposes severe restrictions on the possible collisions/deformations. And allows to prove some bounds on the variation of classical invariants in collisions. We consider in details the δ = const deformations of ordinary multiple point, the deformation of a singularity into the collection of ordinary multiple points and the deformation of the type x + y into a collection of Ak’s.
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