Algebraic Varieties

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Cambridge University Press, Sep 9, 1993 - Mathematics - 163 pages
In this book, Professor Kempf gives an introduction to the theory of algebraic varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject, which will be easily accessible to all newcomers to algebraic varieties.
 

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An excellent textbook for the more mature student (graduate+). It's very short yet contains all the important information in modern algebraic geometry. From the basic definition of algebraic varieties (as the name suggests) through cohomologies of sheaves and some of their applications (Riemann-Roch theorem etc.).
The material is presented very clearly, yet requires a serious effort from the reader in order to understand it fully.
One point - if you need to actually solve problems or work with algebraic geometry it's a good idea to have on hand a more detailed reference (e.g. Hartshorne) to fill in gaps where you need them.
 

Contents

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