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Algebraic geometry --- Curves, Algebraic --- Curves, Plane --- Geometry, projective

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Spline theory. --- Approximation theory. --- Surfaces --- Curves

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Geometry, Projective --- Curves, Plane --- Curves, Algebraic --- 512.77 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Projective geometry --- Geometry, Modern --- Higher plane curves --- Plane curves --- Algebraic curves --- Algebraic varieties --- Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties --- 512.77 Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties

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The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. Included is an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. The Mordell-Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights into the arithmetic of curves of genus 2.

Curves, Algebraic. --- Algebraic varieties. --- Varieties, Algebraic --- Geometry, Algebraic --- Linear algebraic groups --- Algebraic curves --- Algebraic varieties --- Curves, Algebraic --- 512.75 --- 512.75 Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions --- Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions

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514 --- kegels --- meetkunde --- wiskunde --- Conic sections --- Curves, Plane --- Geometry, Plane --- Mathematics --- Ellipse --- Geometry, Analytic --- Parabola