This article is cited in 2 papers

A filtration in the three-dimensional Cremona group

M. A. Frumkin


Abstract: 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.

UDC: 513.015.7

MSC: 14E05

Received: 18.05.1972

 English version: Mathematics of the USSR-Sbornik, 1973, 19:2, 191–208

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