Cremona group

（重定向自Cremona transformation）

In algebraic geometry, the Cremona group, introduced by Cremona (1863, 1865), is the group of birational automorphisms of the n-dimensional projective space over a field k. It is denoted by Cr(P(k)) or Bir(P(k)) or Cr_n(k).

The Cremona group is naturally identified with the automorphism group Aut_k(k(x₁, ..., x_n)) of the field of the rational functions in n indeterminates over k, or in other words a pure transcendental extension of k, with transcendence degree n.

单词	Cremona transformation
释义	Cremona transformation 英语百科 Cremona group （重定向自Cremona transformation） In algebraic geometry, the Cremona group, introduced by Cremona (1863, 1865), is the group of birational automorphisms of the n-dimensional projective space over a field k. It is denoted by Cr(P(k)) or Bir(P(k)) or Cr_n(k). The Cremona group is naturally identified with the automorphism group Aut_k(k(x₁, ..., x_n)) of the field of the rational functions in n indeterminates over k, or in other words a pure transcendental extension of k, with transcendence degree n.
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