Total blow-ups of modules and universal flatifications

TL;DR

This paper investigates the projective spectrum of the Rees algebra of a module, providing a universal property characterization and applications to universal flatifications and birational morphisms.

Contribution

It introduces a new universal property for the projective spectrum of the Rees algebra of a module and applies it to flatifications and birational morphisms.

Findings

Characterization of the projective spectrum via a universal property

Descriptions of universal flatifications of modules

Applications to birational projective morphisms

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.