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 ...
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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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Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $150.29, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $159.66, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2010 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
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2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $182.52, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2010 by Springer.
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2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $231.03, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2010 by Springer.
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2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $99.39, very good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1998 by Springer.
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This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 600grams, ISBN: 9783540546818.
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $150.29, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1997 by Springer.
Add this copy of Algebraic Geometry III: Complex Algebraic Varieties to cart. $159.66, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1997 by Springer.
