Irreducibility criterion for algebroid curves
Commutative Algebra
2011-02-16 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1009.2420,
title = {Irreducibility criterion for algebroid curves},
author = {Takafumi Shibuta},
journal= {arXiv preprint arXiv:1009.2420},
year = {2011}
}
Comments
20 pages, v3: major revision