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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 (Encyclopaedia of Mathematical Sciences)

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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 (Encyclopaedia of Mathematical Sciences)

4.85 76,399 ratings · 3,501 reviews
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Overview: 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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Pages 270
Publisher Springer
Published December 16, 1997
ISBN 2643844
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Igor R. Shafarevich writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Igor R. Shafarevich lives with their spouse and a very vocal rescue cat.

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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Sandra Diaz
Sandra Diaz September 13, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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