Total blow-ups of modules and universal flatifications

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.

KEYWORDS:

• Birational morphism
• blow-up
• flatification
• Rees algebra
• universal property

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 14A15
• Secondary: 13A30
• 13C12
• 14E05

Acknowledgments

I would like to thank David Rydh for all our invaluable discussions and Runar Ile for his careful reading and helpful comments.