Equivalent birational embeddings II: divisors

TL;DR

This paper investigates Cremona equivalence of divisors in projective space, producing infinitely many non-equivalent embeddings for varieties up to dimension 14 and characterizing certain rational hypersurfaces.

Contribution

It introduces new non-equivalent divisorial embeddings and provides a characterization of Cremona equivalence for rational hypersurfaces.

Findings

Infinitely many non-equivalent divisorial embeddings for varieties up to dimension 14.

Characterization of surfaces Cremona equivalent to a plane.

Analysis of Cremona equivalence in plane curves and rational hypersurfaces.

Abstract

Two divisors in $\P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. We produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14. Then we study the special case of plane curves and rational hypersurfaces. For the latter we characterise surfaces Cremona equivalent to a plane.