Algebraic Geometry III: Encyclopedia of Mathematical Science - Couverture rigide

Couverture rigide

ISBN 10 : 3540546812 ISBN 13 : 9783540546818

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1997

Synopsis

Starting with the end of the seventeenth century, one of the most interesting directions in mathematics (attracting the attention as J. Bernoulli, Euler, Jacobi, Legendre, Abel, among others) has been the study of integrals of the form r dz l Aw(T) = -, TO W where w is an algebraic function of z. Such integrals are now called abelian. Let us examine the simplest instance of an abelian integral, one where w is defined by the polynomial equation (1) where the polynomial on the right hand side has no multiple roots. In this case the function Aw is called an elliptic integral. The value of Aw is determined up to mv + nv, where v and v are complex numbers, and m and n are 1 2 1 2 integers. The set of linear combinations mv+ nv forms a lattice H C C, and 1 2 so to each elliptic integral Aw we can associate the torus C/ H. 2 On the other hand, equation (1) defines a curve in the affine plane C = 2 2 {(z, w)}. Let us complete C2 to the projective plane lP' = lP' (C) by the addition of the "line at infinity", and let us also complete the curve defined 2 by equation (1). The result will be a nonsingular closed curve E C lP' (which can also be viewed as a Riemann surface). Such a curve is called an elliptic curve.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 1997
• Langue: anglais
• ISBN 10: 3540546812
• ISBN 13: 9783540546818
• Reliure: Relié
• Nombre de pages: 270
• Éditeur: Parshin A.N., Shafarevich I.R.
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne