ARITHMETIC MACAULAYFICATION OF PROJECTIVE SCHEMES

Dedicated to Wolmer Vasconcelos on the occasion of his sixty fifth birthday. Abstract. In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. We discuss the existence of an arithmetic Macaulayfication for projective schemes. We give a simple neccesary and sufficient condition for nonsingular projective varieties to possess an arithmetic Macaulayfication (Theorem 1.5). We also show that this condition is sufficient in general, but give examples to show that it is not in general necessary. We further consider Rees algebras Rλ(I) = R[Iλt] (truncated Rees algebras) associated to a homogeneous ideal I and show that they are Cohen-Macaulay for large λ in some important cases (Theorem 2.1 and Corollary 2.2.1). In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. In the first part of the paper, we discuss the problem of arithmetic Macaulayfication of projective schemes. This is a globalization of the problem of arithmetic Macaulayficatio