A new Invariant for Plane Curve Singularities
Abstract
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 γ 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 γa, 0 <= a <= 1, with γ1=γ. In the present paper we compute (respectively give bounds for) these invariants for semiquasihomogeneous singularities.
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