Algebraic Geometry I

Affine and projective varieties, Nullstellensatz. Zariski topology. Rational functions and morphisms. Normal varieties. Normalization. Differentials and non-singularity. Jacobian criterion. Blow-up. Rational maps. Curves. Non-singular curves and function fields. Intersection theory in projective spaces; Bezout’s theorem.

References:
HARRIS, J. – Algebraic Geometry – A First Course, GTM 133, Springer-Verlag, 1992.
HARTSHORNE, R. – Algebraic Geometry. Berlin, Springer, 1977.
SEMPLE, J.G. e ROTH, L. – Algebraic Geometry, Oxford University Press, 1949.
SHAFAREVICH, I. – Basic Algebraic Geometry. Berlin, Springer-Verlag, 1974.