Read Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians

Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians

Igor R. Shafarevich

4.9/5 (22613 ratings)

Description: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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians. To get started finding Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 270

Format: PDF, EPUB & Kindle Edition

Publisher: Springer

Release: 1997

ISBN: 3540546812

Description: 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians. To get started finding Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians

Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians

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