Cremona group

The Cremona group is a fundamental concept in algebraic geometry, specifically regarding the study of rational transformations in projective space. In particular, the Cremona group \( \text{Cr}(n) \) refers to the group of birational transformations of \( \mathbb{P}^n \), the \( n \)-dimensional projective space over a field (often taken to be the complex numbers or other algebraically closed fields).