Abelian Functions Abel's Theorem and the Allied Theory of Theta Functions [Paperback]

Baker's 1897 classic book on algebraic geometry and allied theory.In our century, the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched classical algebraic geometry and seemed to have replaced its somewhat naive language. Written in 1897, this classic book, however, stresses algebraic geometry's continuing relevance.In our century, the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched classical algebraic geometry and seemed to have replaced its somewhat naive language. Written in 1897, this classic book, however, stresses algebraic geometry's continuing relevance.Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched it and seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This classic book, written in 1897, covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.1. The subject of investigation; 2. The fundamental functions on a Riemann surface; 3. The infinities of rational functions; 4. Specification of a general form of Riemann's integrals; 5. Certain forms of the fundamental equation of the Riemann surface; 6. Geometrical investigations; 7. Coordination of simple elements; 8. Abel's theorem; 9. Jacobi's inversion problem; 10. Riemann's theta functions; 11. The hyperelliptic case of Riemann's theta functions; 12. A particular form of Riemann surface; 13. Radical functions; 14. Factorial functions; 15. Relations lÃ