A study of a family of monomial ideals.

In this paper, we study a family of rational monomial parametrizations. We investigate a few structural properties related to the corresponding monomial ideal J generated by the parametrization. We first find the implicit equation of the closure of the image of the parametrization. Then we provide a minimal graded free resolution of the monomial ideal J, and describe the minimal graded free resolution of the symmetric algebra of J. Finally, we provide a method to compute the defining equations of the Rees algebra of J using three moving planes that follow the parametrization. [ABSTRACT FROM AUTHOR]