Jacobian pairs

Details Jacobian pairs Jacobian pairs

2002-09-13

arxiv.org/abs/math/0209159v1

Mathematics

Commutative Algebra

latex, 41 pages

Scientific paper

We study meromorphic jacobian pairs, i.e., pairs of polynomials in one variable, with coefficients meromorphic series in a second variable, whose jacobian relative to the two variables depends only on the second variable. We pose two meromorphic jacobian conjectures about such pairs, one of which is in terms of an invariant of the pair which we call the beta invariant. These conjectures are shown to imply the bivariate algebraic jacobian conjecture which predicts that two bivariate polynomials generate the polynomial ring if their jacobian is a nonzero constant. As another technique for studying the jacobian conjecture we revisit the Newton polygon.

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