Total blow-ups of modules and universal flatifications

Abstract

Abstract. We study the projective spectrum of the Rees algebra of a module, and characterize it by a universal property. As applications, we give descriptions of universal flatifications of modules and of birational projective morphisms.

An intrinsic definition of the Rees algebra of a module

“…The intrinsic definition given in the present note is also used in [15] where we describe the projective spectrum of the Rees algebra of a module and show that it has a universal property that generalizes the classical blow-up. In that paper we also show that this generalized blow-up has useful applications in the theory of flatifications of modules and for describing birational projective morphisms of schemes.…”