Irreducibility criterion for algebroid curves

Shibuta, Takafumi

doi:10.1090/S0025-5718-2012-02607-X

Irreducibility criterion for algebroid curves

Author: Takafumi Shibuta
Journal: Math. Comp. 82 (2013), 531-554
MSC (2010): Primary 14H50, 14Q05; Secondary 14H20, 13F25
DOI: https://doi.org/10.1090/S0025-5718-2012-02607-X
Published electronically: June 4, 2012
MathSciNet review: 2983035
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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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