This book is about modern algebraic geometry. The title "A Royal
Road to Algebraic Geometry" is inspired by the famous anecdote
about the king asking Euclid if there really existed no simpler way
for learning geometry, than to read all of his work "Elements."
Euclid is said to have answered: ""There is no royal road to
geometry" "
The book starts by explaining this enigmatic answer, the aim of
the book being to argue that indeed, in some sense" there is" a
royal road to algebraic geometry.
From a point of departure in algebraic curves, the exposition
moves on to the present shape of the field, culminating with
Alexander Grothendieck's theory of schemes. Contemporary
homological tools are explained.
The reader will follow a directed path leading up to the main
elements of modern algebraic geometry. When the road is completed,
the reader is empowered to start navigating in this immense field,
and to open up the door to a wonderful field of research. The
greatest scientific experience of a lifetime
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