Geodesic
A~filtration in the three-dimensional Cremona group
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 191-208

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In this paper we introduce the concept of the genus of a birational mapping of nonsingular three-dimensional algebraic varieties over a field of characteristic 0 and prove that the automorphisms whose genus is at most a fixed number form a group. We also prove that a birational morphism of nonsingular three-dimensional varieties splits into a composition of a map which is an inverse to a morphism of genus 0 and monoidal transformations. Bibliography: 9 titles. 
@article{SM_1973_19_2_a3,
     author = {M. A. Frumkin},
     title = {A~filtration in the three-dimensional {Cremona} group},
     journal = {Sbornik. Mathematics},
     pages = {191--208},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_2_a3/}
}
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M. A. Frumkin. A~filtration in the three-dimensional Cremona group. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 191-208. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a3/