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Lectures about the geometric theory of equations and algebraic functions. 1: Vol. \(I+II\). 2: Vol. \(III+IV\). New ed.. (Lezioni sulla teoria geometrica delle equazione e delle funzioni algebriche. 1: Vol. I e II. 2: Vol. III e IV. Ristampa). (Italian) Zbl 0571.51001
Collana di Matematica, 5. Bologna: Nicola Zanichelli. XIV, 1111 p.; 868 p. L. 96.000.00 (1985).
This is a classical book for Projective and Differential geometry; the four volumes, first edited in 1915, 1918, 1924, 1934 [Vol. \(I+II\) \((1915+1918)\), JFM 46.0941.11; Vol. III (1924), JFM 51.0508.03; Vol. IV (1934; Zbl 0009.15904 and JFM 60.1058.03)] are only now edited together. Authors’ aspiration for a plain, rigorous and independent exposition determinated the massiveness of the book.
Without structural or detail changes, the work remained more than fifty years an excellent monograph on the following subjects: (1st book) Projective and Analytical geometry; (2nd book) Correspondence principle and Application; (3rd book) Plane Curves; (4th book) Singularities for Algebraical Curves and Surfaces; (5th book) Curves and Algebraic Maps; (6th book) Elliptic and Abelian Functions.
The bibliography clearly presents the source books.
The work may be used for some other domains: History of Mathematics, Algebraic Geometry, Functions of a Complex Variable.
Reviewer: D.Brânzei

51-02 Research exposition (monographs, survey articles) pertaining to geometry
51A05 General theory of linear incidence geometry and projective geometries
14E05 Rational and birational maps
14H05 Algebraic functions and function fields in algebraic geometry
14E07 Birational automorphisms, Cremona group and generalizations
30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces