Irreducibility criterion for algebroid curves

Takafumi Shibuta

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)531-554
Number of pages24
JournalMathematics of Computation
Volume82
Issue number281
DOIs
Publication statusPublished - Jan 17 2013

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Tropical Geometry
Resolution of Singularities
Irreducibility
Algebraically closed
Analogue
Curve
Geometry
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Irreducibility criterion for algebroid curves. / Shibuta, Takafumi.

In: Mathematics of Computation, Vol. 82, No. 281, 17.01.2013, p. 531-554.

Research output: Contribution to journalArticle

Shibuta, Takafumi. / Irreducibility criterion for algebroid curves. In: Mathematics of Computation. 2013 ; Vol. 82, No. 281. pp. 531-554.
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