Both books a small and elementary, ideal for the first introduction. AbeBooks.com: Algebraic Curves (9780387903613) by Walker, Robert J. and a great selection of similar New, Used and Collectible Books available now at great prices. This book was written to furnish a starting point for the study of algebraic geometry. Let us now take, as an example, the diophantine equation Algebraic Curves (COMPLETE) Robert J. Walker This introduction to algebraic geometry examines how the more recent abstract concepts relate to traditional analytical and geometrical problems. A good classical book is Walker, Algebraic curves, Princeton, 1950. So far we have considered only equations of degree at most 2. Algebraic curves Robert J. Walker This introduction to algebraic geometry examines how the more recent abstract concepts relate to traditional analytical and geometrical problems. Algebraic Curves by Robert J. Walker (Author) 3.9 out of 5 stars 3 ratings

Thus a cubic with a double point is always rational. A more modern one on the same elementary level is Gerd Fischer, Plane algebraic curves, AMS, 2001.

Algebraic Curves - An Introduction to Algebraic Geometry, by William Fulton. Because of the group structure on the integer solutions of x 2 − dy 2 = 1, we were able to employ algebraic methods to find these solutions. By the way, as Walker makes clear, an irreducible curve of degree d, with a single singular point of multiplicity d-1, is already rational, and can be parametrized using Bezout's theorem.


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