Syzygies and the Rees algebra

Abstract: Let be linearly independent homogeneous polynomials in the standard -graded ring with the same degree and no common divisors. This defines a morphism . The Rees algebra of the ideal is the graded -algebra which can be described as the image of an -algebra homomorphism : . This paper discusses one result concerning the structure of the kernel of the map and its relation to the problem of finding the implicit equation of the image of the map given by , , . In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox. [Copyright &y& Elsevier]