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 | 8 |
The Logarithmic Function | 11 |
An Easygoing Realization Cross Ratio | 20 |
著作権 | |
他の 29 セクションは表示されていません
多く使われている語句
1-dimensional A₁ barycenter boundary C₁ called chamber of type Chapter compactification complex configuration space congruence subgroup consider corresponding D₁ defined denoted differential equation distinct points divisor domain double cover Dr+1 elliptic curves elliptic function embedding equivalence relation FIGURE formula four points given H₁ H₂ holomorphic homogeneous coordinates hypergeometric differential equation hypergeometric functions hypergeometric integrals hyperplanes integrals of type intersection number invariant inverse involution isomorphism juzu K3 surface LEMMA linear linearly independent loaded cycles log C₂ matrix mirrors modular interpretation monodromy group non-singular obtained path plane projective line projective space PROOF PROPOSITION quadric quotient space rational numbers realization reflection roots Schwarz map Schwarz triangle six lines solutions subgroup symmetric t₁ tetrahedron theorem theta functions transformation u₁ w₁ w₂ zero