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The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source.
The first volume appeared 1985 as vol. 267 of the same series.
The first volume appeared 1985 as vol. 267 of the same series.
From the reviews: "A comprehensive account of the deepest results of the geometry of algebraic curves that were obtained in the second half of the 20th century using some of the more advanced techniques of abstract algebraic geometry ... . at the end of every chapter there bibliographical notes that guide the reader to the original literature and further developments and sets of exercises that complement the theory ... . an immediate standard reference for researchers and students working on the geometry of algebraic curves ... ." (Felipe Zaldivar, The Mathematical Association of America, July, 2011)