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Algebraic Geometry and the Theory of Curves

by Bump D

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A self-contained introduction to algebraic geometry and curves

$59.40 USD
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Hardcover New English

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AlbakiReads Editorial

A self-contained introduction to algebraic geometry and curves

Designed as a graduate-level text, the book develops the fundamentals of algebraic geometry alongside the commutative algebra used in that development. It also gives extended attention to local algebra and ramification theory, offering a route from foundational material into selected deeper topics. The final section turns to algebraic curves, with coverage that includes the Riemann–Roch theorem, elliptic curves, zeta functions of curves over finite fields, and the Riemann hypothesis for elliptic curves. This progression makes the volume a focused bridge between core algebraic-geometric tools and several central subjects in curve theory.

Good fit for readers who enjoy

  • Graduate students seeking a structured introduction to algebraic geometry.
  • Mathematics readers interested in the algebraic foundations of curve theory.
  • Readers looking for a text that includes local algebra, ramification, and elliptic-curve topics.

Themes

Algebraic geometryCommutative algebraLocal algebra and ramification theoryAlgebraic curves and elliptic curves

Based on publisher information and book metadata.

Book overview

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann-Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.

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