Algebraic Geometry is the study
of algebraic varieties,
that is sets of common zeros of some
polynomials. Historically this study is
performed by the
analysis of geometrical, algebraic, topological,
differential, analytic and numerical properties.
Such richness of points of view makes Algebraic Geometry one of the most
fascinating and central areas of
mathematics. Many famous
problems
in mathematics, like Fermat's
Last Theorem, have been solved with the
essential use of Algebraic Geometry. The
course introduces to basic properties of affine
and projective algebraic varieties,
to maps among them, to their local geometry and
to the theory of divisors and linear systems.
OUTLINE
OF CONTENT
Classical theory of algebraic varieties, affine and projective, over
algebraically closed fields. Local geometry, normalization.
Divisors, linear systems and associated morfisms (time
permetting).
SUGGESTED
BOOKS:
We will follow
closely the lecture notes written by L. Caporaso (the
notes will be given in class).
We also suggest the following classical textbooks: *
R. Hartshorne, Algebraic
geometry,Graduate Texts in Math. No. 52.
Springer-Verlag, New York-Heidelberg, 1977. * I. Shafarevich, Basic algebraic geometry vol.
1, Springer-Verlag, New York-Heidelberg, 1977. * J.
Harris, Algebraic
geometry (a first course), Graduate Texts in Math. No.
133. Springer-Verlag, New York-Heidelberg, 1977.
