Irreducibility criterion for algebroid curves

Shibuta, Takafumi

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

Irreducibility criterion for algebroid curves
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Math. Comp. 82 (2013), 531-554 Request permission

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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