A new Invariant for Plane Curve Singularities

Details A new Invariant for Plane Curve Singularities A new Invariant for Plane Curve Singularities

2004-09-21

arxiv.org/abs/math/0409404v2

Rend. Sem. Mat. Univ. Politec. Torino 63 (2005), no. 1, 15--42

Mathematics

Algebraic Geometry

Some minor modifications of the original paper

Scientific paper

Greuel, Lossen and Shustin gave a general sufficient numerical condition for the T-smoothness (smoothness and expected dimension) of equisingular families of plane curves. This condition involves a new invariant \gamma for plane curve singularities, and it is conjectured to be asymptotically proper. In math.AG/0308247, similar sufficient numerical conditions are obtained for the T-smoothness of equisingular families on various classes surfaces. These conditions involve a series of invariants \gamma_a, 0 <= a <= 1, with \gamma_1=\gamma. In the present paper we compute (respectively give bounds for) these invariants for semiquasihomogeneous singularities.

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