# Théorie des fonctions algébriques de deux variables indépendantes, Volumes I and II: Second Edition

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*Émile Picard; Georges Simart*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

This single volume contains the two original volumes, which were written ten
years apart from each other. The first volume is a preliminary discussion of
multiple integrals and the associated geometry. The authors treat the
connections with algebraic surfaces and integrals of total differentials. The
last two chapters of Volume I are devoted to the study of numerical invariants
introduced by Clebsch and Noether, and to the double integrals attached to
them.

The second volume is a more developed discussion of both the geometry and the
analysis of algebraic functions, including results obtained by Picard,
Castelnuovo, and Enriques in the time after the publication of Volume I. Most
of the geometry revolves around linear systems of curves, either in the plane
or on a surface. There is also a special chapter on the geometry of
hyperelliptic surfaces. The major part of the analysis in Volume II is
centered on integrals of the second kind, including their periods and the
number of distinct such integrals in specific instances. The book concludes
with a long section of notes on various interesting topics.