Algebraic Geometry II

Sheaves and schemes. Morphisms of schemes. Sheaves of module and coherent sheaves. Cartier & Weil divisors. Line bundles and Cartier divisor classes. Differentials. Cohomology of coherent sheaves. Cohomology of the projective space. Serre’s duality theorem. Riemann-Roch theorem for curves and surfaces, some applications.

References:
ARBARELLO, E.; CORNALBA, M; GRIFFTHS, P.A. e HARRIS, J. – Geometry of algebraic curves. Vol. I. Grundlehren der Mathematischen Wissenschaften, 267. Springer-Verlag, New York, 1985.
GRIFFITHS, P. e HARRIS, J. – Principles of Algebraic Geometry. New York, Wiley-Interscience, 1978.
HARTSHORNE, R. – Algebraic Geometry. Berlin, Springer, 1977.
MUMFORD, D. – The Red Book of Varieties and Schemes. Berlin, Springer-Verlag, 1988.