Equivalent birational embeddings
Massimiliano Mella, Elena Polastri

TL;DR
This paper proves that any two birational embeddings of a projective variety into projective space of dimension at least r+2 are equivalent through Cremona transformations, establishing a fundamental relation between such embeddings.
Contribution
It establishes that all birational embeddings of a projective variety into sufficiently high-dimensional projective space are Cremona equivalent.
Findings
Any two birational embeddings in ^n, n e2 r+2, are Cremona equivalent.
The result applies to varieties over algebraically closed fields.
Provides a unifying view of birational embeddings via Cremona transformations.
Abstract
Let be a projective variety of dimension over an algebraically closed field. It is proven that two birational embeddings of in , with are equivalent up to Cremona transformations of .
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