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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The computational complexity of the resolution of plane curve singularities
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by Jeremy Teitelbaum PDF
Math. Comp. 54 (1990), 797-837 Request permission

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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • 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