Algebraic geometry is a fascinating branch of mathematics that
combines methods from both, algebra and geometry. It transcends the
limited scope of pure algebra by means of geometric construction
principles. Moreover, Grothendieck s schemes invented in the late
1950s allowed the application of algebraic-geometric methods in
fields that formerly seemed to be far away from geometry, like
algebraic number theory. The new techniques paved the way to
spectacular progress such as the proof of Fermat s Last Theorem by
Wiles and Taylor.
The scheme-theoretic approach to algebraic geometry is explained
for non-experts. More advanced readers can use the book to broaden
their view on the subject. A separate part deals with the necessary
prerequisites from commutative algebra. On a whole, the book
provides a very accessible and self-contained introduction to
algebraic geometry, up to a quite advanced level.
Every chapter of the book is preceded by a motivating
introduction with an informal discussion of the contents. Typical
examples and an abundance of exercises illustrate each section.
This way the book is an excellent solution for learning by yourself
or for complementing knowledge that is already present. It can
equally be used as a convenient source for courses and seminars or
as supplemental literature."
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