Publication: On ν-quasi-ordinary power series: factorization, Newton trees and resultants
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Publication Date
2011
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American Mathematical Society
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Abstract
The concept of ν-quasi-ordinary power series, which is a generalization of quasi-ordinary power series, was first introduced by H. Hironaka. In the paper under review, the authors study ν-quasi-ordinary power series and give a factorization theorem for ν-quasi-ordinary power series in the first part. The proof of the theorem uses Newton maps. In the second part of the paper, using the factorization theorem, they introduce the Newton tree to encode the Newton process for any hypersurface singularity defined by a power series germ as in Notation 1.1. Finally, the authors describe a condition for two ν-quasi-ordinary power series to have an "intersection multiplicity " by using Newton trees and they can also compute this generalized intersection multiplicity, resultants and discriminant.
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Papers from the Conference on Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held in Jaca, June 22–26, 2009
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