The Rees Algebra of a monomial plane parametrization

Abstract

Abstract. We compute a minimal bigraded resolution of the Rees Algebra associated to a proper rational parametrization of a monomial plane curve. We describe explicitly both the bigraded Betti numbers and the maps of the resolution in terms of a generalized version of the Euclidean Algorithm. We also explore the relation between pencils of adjoints of the monomial plane curve and elements in a suitable piece of the defining ideal of the Rees Algebra.

On a conjecture of Vasconcelos via Sylvester forms

“…For the binary case (i.e., for n = 2) a result of M. Rossi and I. Swanson ([6, Proposition 1.9]) gives an affirmative answer to the conjecture. Recently, different proofs were established in the binary case of monomials of the same degree as a consequence of work by T. Benitez and C. D'Andrea ( [1]), and independently, of work by the present second and third authors ( [7]).…”