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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 62,964 ratings · 1,266 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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I was completely blown away. 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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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Deborah Rodriguez
Deborah Rodriguez June 26, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Christopher Anderson
Christopher Anderson May 05, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Edward Gomez
Edward Gomez February 12, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Kenneth Harris April 26, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Ryan Lee
Ryan Lee March 13, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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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. I am now a lifelong fan of this author.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Joshua Hernandez November 18, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
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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. Worth every moment spent reading.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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