### Abstract

Let X be a compactification of C^{2} such that a polynomial p can be extended to a regular mapping p: X → CP^{1}. If generic fibers of p are irreducible, then we show that the number of reducible fibers is less than the number of horizontal components of the curve X-C^{2}. If p is rational, then the restriction of p to every horizontal component except one is a one-to-one mapping.

Original language | English (US) |
---|---|

Pages (from-to) | 285-295 |

Number of pages | 11 |

Journal | Pacific Journal of Mathematics |

Volume | 154 |

Issue number | 2 |

State | Published - 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*154*(2), 285-295.

**Two remarks on polynomials in two variables.** / Kaliman, Shulim.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 154, no. 2, pp. 285-295.

}

TY - JOUR

T1 - Two remarks on polynomials in two variables

AU - Kaliman, Shulim

PY - 1992

Y1 - 1992

N2 - Let X be a compactification of C2 such that a polynomial p can be extended to a regular mapping p: X → CP1. If generic fibers of p are irreducible, then we show that the number of reducible fibers is less than the number of horizontal components of the curve X-C2. If p is rational, then the restriction of p to every horizontal component except one is a one-to-one mapping.

AB - Let X be a compactification of C2 such that a polynomial p can be extended to a regular mapping p: X → CP1. If generic fibers of p are irreducible, then we show that the number of reducible fibers is less than the number of horizontal components of the curve X-C2. If p is rational, then the restriction of p to every horizontal component except one is a one-to-one mapping.

UR - http://www.scopus.com/inward/record.url?scp=84974005685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974005685&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84974005685

VL - 154

SP - 285

EP - 295

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -