Two remarks on polynomials in two variables

Shulim Kaliman

Vol. 154 (1992), No. 2, 285–295

DOI: 10.2140/pjm.1992.154.285

Abstract

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.

Mathematical Subject Classification 2000

Primary: 32J15

Secondary: 14E35, 32A15, 32J05

Milestones

Received: 27 December 1990

Published: 1 June 1992