Geodesic
Defining relations for the Cremona group of the plane
Izvestiya. Mathematics , Tome 21 (1983) no. 2, pp. 211-268.

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By methods of the geometry of rational surfaces and the topology of graphs and cell complexes connected with them, the author establishes defining relations, connecting projectives, and quadratic transformations, for the group of birational transformations of the plane over an algebraically closed field. Bibliography: 11 titles. 
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M. Kh. Gizatullin. Defining relations for the Cremona group of the plane. Izvestiya. Mathematics , Tome 21 (1983) no. 2, pp. 211-268. http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a1/

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