Weighted homogeneous polynomials and the Jacobian
Abstract
This thesis was motivated by Abhyankar's work on the Jacobian Conjecture. We give here a study on how the Jacobian acts on weighted homogeneous polynomials over an algebraically closed field of characteristic zero and use these results to determine properties of positively weighted homogeneous pairs (F,G) with J(F,G) = &thetas; F or J(F,G) = &thetas; F2. Most notably, we provide a general example for each of these cases demonstrating the impossibility of extending certain results given for negative weights by Abhyankar in [4].
Degree
Ph.D.
Advisors
Abhyankar, Purdue University.
Subject Area
Mathematics
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