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  1. Home
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  3. Methods of Algebraic Geometry
  • Cited by 28
Publisher:
Cambridge University Press
Online publication date:
February 2010
Print publication year:
1994
Online ISBN:
9780511623899
DOI:
https://doi.org/10.1017/CBO9780511623899
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
Cambridge Mathematical Library
Information

Book description

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties in spaces of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. The ground field is without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers, a sound algebraic basis for classical geometry is provided. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

Reviews

‘This treatise … is notable for its clarity of treatment and for the rigour of its demonstrations, and will repay careful study even in those parts which deal with matters generally considered familiar.’

Source: Nature

‘The book is well set out, and is a pleasure to work through.’

Source: The Times Literary Supplement

‘Motivations are given. Examples of significant and useful varieties are numerous. All the algebra needed is given, and, what is more, these books tell how to translate geometry into algebra, and conversely.’

Source: Bulletin of the American Mathematical Society

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