Hypergeometric Functions, My Love: Modular Interpretations of Configuration SpacesVieweg+Teubner Verlag, 1997/04/16 - 292 ページ 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. |
目次
Configuration Spaces The Simplest Case | 3 |
The Logarithmic Function | 11 |
An Easygoing Realization Cross Ratio | 20 |
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多く使われている語句
1-dimensional a(ijk barycenter boundary C(ij C₁ C₂ called chamber of type Chapter compactification complex configuration space congruence subgroup consider corresponding D₁ defined denoted differential equation distinct points divisor domain double contour loop double cover elliptic curves elliptic function embedding equivalent f₁ FIGURE fixed points formula four points given H₁ holomorphic homogeneous coordinates hypergeometric differential equation hypergeometric functions hypergeometric integrals hyperplanes integrals of type intersection number invariant involution isomorphism juzu K3 surface LEMMA linear linearly independent loaded cycles matrix mirrors modular interpretation monodromy group non-singular Note obtained path projective plane projective space PROOF PROPOSITION quadric quotient space realization reflection relation roots Schwarz map Schwarz triangle six lines solutions subset symmetric group tetrahedron theta functions transformation w₁ zero ди レー