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The classical story - of the hypergeometric functions, the configuration space of 4 points on the projective line, elliptic curves, elliptic modular functions and the theta functions - now evolves, in this book, to the story of hypergeometric funktions in 4 variables, the configuration space of 6 points in the projective plane, K3 surfaces, theta functions in 4 variables.
This modern theory has been established by the author and his collaborators in the 1990's; further development to different aspects is expected.
It leads the reader to a fascinating 4-dimensional world.
The author tells the story casually and visually in a plain language, starting form elementary level such as equivalence relations, the exponential function, ... Undergraduate students should be able to enjoy the text.
Part 1: The Story of the Configuration Space X (2,4) of Four Points on the Projective Line:
Configuration Spaces - The Simplest Case; Elliptic Curves; Modular Interpretations of X (2,4); Hypergeometric Integrals and Loaded Cycles.
Part 2: The Story of the Configuration Space X (2,n) of n Points on the Projective Line:
The Configuration Space X (2,5); Modular Interpretation of the Configuration Space X (2,n); The Configuration Space X (3,6); Hypergeometric Functions of Type (3,6); Modular Interpretation of the Configuration Space X (3,6)
Masaaki Yoshida ist Professor für Mathematik an der Kyushu Universität, Japan.