Algebraic Geometry II
Beams and schemas. Schema morphisms. Module bundles and coherent bundles. Cartier and Weil divisors. Fibrations on lines and classes of Cartier divisors. Differentials. Cohomology of coherent bundles. Cohomology of projective space. Serre’s duality theorem. Riemann-Roch theorem for curves and surfaces, some applications.
References:
ARBARELLO, E.; CORNALBA, M; GRIFFTHS, P.A. and HARRIS, J. – Geometry of algebraic curves. Vol. I. Grundlehren der Mathematischen Wissenschaften, 267. Springer-Verlag, New York, 1985.
GRIFFITHS, P. and 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.
ARBARELLO, E.; CORNALBA, M; GRIFFTHS, P.A. and HARRIS, J. – Geometry of algebraic curves. Vol. I. Grundlehren der Mathematischen Wissenschaften, 267. Springer-Verlag, New York, 1985.
GRIFFITHS, P. and 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.
* Basic syllabus. The teacher has the autonomy to make any changes.