ar X iv : 0 80 5 . 40 83 v 4 [ m at h . A G ] 2 1 A pr 2 00 9
نویسندگان
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. These are also known as equi-normalizable or equi-generic deformations. We restrict primarily to the deformations of singularities with smooth branches. A natural 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 equi-normalizable families. We consider in details deformations of ordinary multiple point, the deformations of a singularity into the collections of ordinary multiple points and deformations of the type x + y into the collections of Ak’s.
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