Irreducibility of lemniscates

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arxiv 1806.10377 v1 pith:75HL45GR submitted 2018-06-27 math.AG

S. Yu. Orevkov This is my paper · ORCID

classification math.AG

keywords lemniscatesalgebraiccomplexcurvesformirreducibilityirreduciblepolynomial

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abstract

We prove that lemniscates (i.e., sets of the form $|P(z)|=1$ where $P$ is a complex polynomial) are irreducible real algebraic curves.