An Algebraic Introduction to Complex Projective Geometry

Released on by Christian Peskine
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  • An Algebraic Introduction to Complex Projective Geometry Book Detail

  • Author : Christian Peskine
  • Release Date : 1843
  • Publisher :
  • Genre : Mathematics
  • Pages : 454
  • ISBN 13 :
  • File Size : 74,74 MB
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An Algebraic Introduction to Complex Projective Geometry by Christian Peskine PDF Summary

Book Description: In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.

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Perspectives on Projective Geometry

Perspectives on Projective Geometry

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Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many