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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].
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
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