A theorem about Cremona maps and symbolic Rees algebras

Abstract

This work is about the structure of the symbolic Rees algebra of the base ideal of a Cremona map. We give sufficient conditions under which this algebra has the "expected form" in some sense. The main theorem in this regard seemingly covers all previous results on the subject so far. The proof relies heavily on a criterion of birationality and the use of the so-called inversion factor of a Cremona map. A pretty long selection of examples of plane and space Cremona maps has been given to test against the conditions of the theorem, with special emphasis on Cohen–Macaulay base ideals.