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Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians - Couverture souple
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.
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Algebraic Geometry III : Complex Algebraic Varieties. Algebraic Curves and Their Jacobians
Edition internationaleVendeur : Sizzler Texts, SAN GABRIEL, CA, Etats-Unis
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Hardcover. Etat : New. Etat de la jaquette : New. 1st Edition. **INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. N° de réf. du vendeur ABE-8061205813
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Algebraic Geometry III
Edité par
Springer Berlin Heidelberg, 2010
ISBN 10 : 3642081185
ISBN 13 : 9783642081187
Neuf
Couverture souple
Vendeur : moluna, Greven, Allemagne
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieti. N° de réf. du vendeur 5047165
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Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians (Encyclopaedia of Mathematical Sciences)
Vendeur : Ria Christie Collections, Uxbridge, Royaume-Uni
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Etat : New. In. N° de réf. du vendeur ria9783642081187_new
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Algebraic Geometry III
Edité par
Springer Berlin Heidelberg Dez 2010, 2010
ISBN 10 : 3642081185
ISBN 13 : 9783642081187
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject. 284 pp. Englisch. N° de réf. du vendeur 9783642081187
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Algebraic Geometry III : Complex Algebraic Varieties Algebraic Curves and Their Jacobians
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2010
ISBN 10 : 3642081185
ISBN 13 : 9783642081187
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783642081187
Quantité disponible : 1 disponible(s)
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Algebraic Geometry III
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2010, 2010
ISBN 10 : 3642081185
ISBN 13 : 9783642081187
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 284 pp. Englisch. N° de réf. du vendeur 9783642081187
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Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians (Encyclopaedia of Mathematical Sciences)
Vendeur : Lucky's Textbooks, Dallas, TX, Etats-Unis
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Etat : New. N° de réf. du vendeur ABLIING23Mar3113020216819
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