Polar quotients and singularities at infinity of polynomials in two complex variables

Płoski, Arkadiusz

doi:10.4064/ap78-1-6

Ann. Polon. Math.

2002

DOI: 10.4064/ap78-1-6

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Polar quotients and singularities at infinity of polynomials in two complex variables

Arkadiusz Płoski

Abstract: Abstract. Using the notion of the maximal polar quotient we characterize the critical values at infinity of polynomials in two complex variables. As an application we give a necessary and sufficient condition for a family of affine plane curves to be equisingular at infinity.

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Polar Invariants of Plane Curve Singularities: Intersection Theoretical Approach

Gwoździewicz¹,

Lenarcik²,

Płoski³

2010

Demonstratio Mathematica

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This article, based on the talk given by one of the authors at the Pierrettefest in Castro Urdiales in June 2008, is an overview of a number of recent results on the polar invariants of plane curve singularities.2000 Mathematics Subject Classification: Primary 32S55; Secondary 14H20. Key words and phrases: plane curve singularity, polar invariant, jacobian Newton polygon, equisingularity, pencil of plane curve singularities.

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Polar Invariants of Plane Curve Singularities: Intersection Theoretical Approach

Gwoździewicz¹,

Lenarcik²,

Płoski³

2010

Demonstratio Mathematica

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Polar invariants of plane curve singularities: intersection theoretical approach

Gwoździewicz¹,

Lenarcik²,

Płoski³

2010

Demonstratio Mathematica

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The gradient of a polynomial at infinity

Chądzyński¹,

Krasiński²

2003

Kodai Math. J.

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scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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Polar quotients and singularities at infinity of polynomials in two complex variables

Abstract: Abstract. Using the notion of the maximal polar quotient we characterize the critical values at infinity of polynomials in two complex variables. As an application we give a necessary and sufficient condition for a family of affine plane curves to be equisingular at infinity.

Cited by 4 publications

References 2 publications

Polar Invariants of Plane Curve Singularities: Intersection Theoretical Approach

Polar Invariants of Plane Curve Singularities: Intersection Theoretical Approach

Polar invariants of plane curve singularities: intersection theoretical approach

The gradient of a polynomial at infinity

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