Resumen de Syzygies and the Rees algebra

David Cox, Jerome William Hoffman, Hao Hao Wang

• Let a,b,c be linearly independent homogeneous polynomials in the standard -graded ring Rk[s,t] with the same degree d and no common divisors. This defines a morphism . The Rees algebra of the ideal I=a,b,c is the graded R-algebra which can be described as the image of an R-algebra homomorphism h: . This paper discusses one result concerning the structure of the kernel of the map h and its relation to the problem of finding the implicit equation of the image of the map given by a, b, c. 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.