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Mathematics of Computation

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The computational complexity of the resolution of plane curve singularities


Author: Jeremy Teitelbaum
Journal: Math. Comp. 54 (1990), 797-837
MSC: Primary 14B05; Secondary 14-04, 14H20, 68Q25
DOI: https://doi.org/10.1090/S0025-5718-1990-1010602-1
MathSciNet review: 1010602
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Abstract: We present an algorithm which computes the resolution of a plane curve singularity at the origin defined by a power series with coefficients in a (not necessarily algebraically closed) field k of characteristic zero. We estimate the number of k-operations necessary to compute the resolution and the conductor ideal of the singularity. We show that the number of k-operations is polynomially bounded by the complexity of the singularity, as measured for example by the index of its conductor ideal. Our algorithm involves calculations over reduced rings with zero divisors, and employs methods of deformation theory to reduce the consideration of power series to the consideration of polynomials.


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DOI: https://doi.org/10.1090/S0025-5718-1990-1010602-1
Article copyright: © Copyright 1990 American Mathematical Society

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