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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Irreducibility criterion for algebroid curves


Author: Takafumi Shibuta
Journal: Math. Comp. 82 (2013), 531-554
MSC (2010): Primary 14H50, 14Q05; Secondary 14H20, 13F25
Published electronically: June 4, 2012
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Abstract: The purpose of this paper is to give an algorithm for deciding the irreducibility of reduced algebroid curves over any algebraically closed field without using resolution of singularities. To do this, we introduce a new notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and we prove an analogue of the the fundamental theorem of tropical geometry.


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Additional Information

Takafumi Shibuta
Affiliation: Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Tokyo 171-8501, Japan
Email: shibuta@rikkyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02607-X
PII: S 0025-5718(2012)02607-X
Received by editor(s): February 23, 2011
Received by editor(s) in revised form: February 25, 2011, and August 16, 2011
Published electronically: June 4, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.