Semi-group conditions for affine algebraic plane curves with more than one place at infinity.

Penelope G. Wightwick

Revista Matemática Complutense (2007)

  • Volume: 20, Issue: 1, page 139-206
  • ISSN: 1139-1138

Abstract

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An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity.

How to cite

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Wightwick, Penelope G.. "Semi-group conditions for affine algebraic plane curves with more than one place at infinity.." Revista Matemática Complutense 20.1 (2007): 139-206. <http://eudml.org/doc/41931>.

@article{Wightwick2007,
abstract = {An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity.},
author = {Wightwick, Penelope G.},
journal = {Revista Matemática Complutense},
keywords = {Curvas algebraicas planas; Polinomios; Variedades afines; Semigrupos; affine algebraic curves; link at infinity},
language = {eng},
number = {1},
pages = {139-206},
title = {Semi-group conditions for affine algebraic plane curves with more than one place at infinity.},
url = {http://eudml.org/doc/41931},
volume = {20},
year = {2007},
}

TY - JOUR
AU - Wightwick, Penelope G.
TI - Semi-group conditions for affine algebraic plane curves with more than one place at infinity.
JO - Revista Matemática Complutense
PY - 2007
VL - 20
IS - 1
SP - 139
EP - 206
AB - An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity.
LA - eng
KW - Curvas algebraicas planas; Polinomios; Variedades afines; Semigrupos; affine algebraic curves; link at infinity
UR - http://eudml.org/doc/41931
ER -

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