Irreducibility criterion for algebroid curves

Details Irreducibility criterion for algebroid curves Irreducibility criterion for algebroid curves

2010-09-13

arxiv.org/abs/1009.2420v3

Mathematics

Commutative Algebra

20 pages, v3: major revision

Scientific paper

The purpose of this paper is to give an algorithm for deciding the irreducibility of reduced algebroid curves over an algebraically closed field of arbitrary characteristic. To do this, we introduce a new notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and then give irreducibility criterion for algebroid curves in terms local tropical varieties. We also give an algorithm for computing the value-semigroups of irreducible algebroid curves. Combining the irreducibility criterion and the algorithm for computing the value-semigroups, we obtain an algorithm for deciding the irreducibility of algebroid curves.

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