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A bound for the Milnor number of plane curve singularities

100%

Płoski A.

Open Mathematics

2014

tom 12

nr 5

688-693

Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

The jump of the Milnor number in the X 9 singularity class

80%

Brzostowski S., Krasiński T.

Open Mathematics

2014

tom 12

nr 3

429-435

The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.

Topology of families of affine plane curves

80%

Vui H., Son P.

Annales Polonici Mathematici

1999

tom 71

nr 2

129-139

We determine bifurcation sets of families of affine curves and study the topology of such families.

Remark on the equisingularity of families of affine plane curves

61%

Vui H., Son P. k.

Annales Polonici Mathematici

1998

tom 68

nr 3

275-280

We give some criteria for the equisingularity of families of affine plane curves.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Open Mathematics

2 Vui H.

1 Brzostowski S.

1 Krasiński T.

1 Płoski A.

1 Son P.

1 Son P. k.

2 2014

1 1999

1 1998

Wyniki wyszukiwania

A bound for the Milnor number of plane curve singularities

The jump of the Milnor number in the X 9 singularity class

Topology of families of affine plane curves

Remark on the equisingularity of families of affine plane curves