Cremona group

In birational geometry, the Cremona group, named after Luigi Cremona, is the group of birational automorphisms of the ${\displaystyle n}$-dimensional projective space over a field ${\displaystyle k}$, also known as Cremona transformations. It is denoted by ${\displaystyle Cr(\mathbb {P} ^{n}(k))}$, ${\displaystyle Bir(\mathbb {P} ^{n}(k))}$ or ${\displaystyle Cr_{n}(k)}$.