Collected papers. Vol. III: Topology of curves and surfaces, and special topics in the theory of algebraic varieties. Edited and with an introduction by M. Artin and B. Mazur.

*(English)*Zbl 0446.14001
Mathematicians of Our Time 12. Cambridge, Massachusetts; London: The MIT Press. xxvi, 480 p. £28.00 (1978).

The papers of this third volume of Zariski’s work were originally published between 1925 and 1966, but the bulk of them are from the ten year period 1928–1937. Thus they were written during the last year of his stay in Rome and his early years at John Hopkins University. The introduction by M. Artin and B. Mazur contains an illuminating discussion of the impact of these papers on the later work of other mathematicians.

The papers themselves may be broadly divided into three sections: (1) solvability by radicals of the equations of plane-algebraic curves, (2) the fundamental group of the residual space of a plane algebraic curve and (3) the topology of the singularities of plane algebraic curves.

In addition three survey articles are reproduced. The first is Zariski’s lecture to the International Congress of Mathematicians at Harvard in 1950 surveying his overall view of algebraic geometry [Zbl 0049.22701]. The second is an introduction to the application of valuation theory to algebraic geometry from lectures given in Rome in 1953. The third on Serre’s coherent sheaves is a report of a seminar at an AMS summer institute in 1954 and is still a good place to find an introduction to algebraic sheaf theory.

The papers themselves may be broadly divided into three sections: (1) solvability by radicals of the equations of plane-algebraic curves, (2) the fundamental group of the residual space of a plane algebraic curve and (3) the topology of the singularities of plane algebraic curves.

In addition three survey articles are reproduced. The first is Zariski’s lecture to the International Congress of Mathematicians at Harvard in 1950 surveying his overall view of algebraic geometry [Zbl 0049.22701]. The second is an introduction to the application of valuation theory to algebraic geometry from lectures given in Rome in 1953. The third on Serre’s coherent sheaves is a report of a seminar at an AMS summer institute in 1954 and is still a good place to find an introduction to algebraic sheaf theory.

Reviewer: David Kirby (Southampton)

##### MSC:

14-03 | History of algebraic geometry |

01A75 | Collected or selected works; reprintings or translations of classics |

14H30 | Coverings of curves, fundamental group |

14E20 | Coverings in algebraic geometry |

12J20 | General valuation theory for fields |

14H20 | Singularities of curves, local rings |