20410462 - GE510 - ALGEBRAIC GEOMETRY 2

Introduce to the study of algebraic geometry, with particular emphasis on beams, schemes and cohomology.

Curriculum

teacher profile | teaching materials

Programme

- Introduction and motivation
- Affine and projective schemes, morphisms and properties
- Diviors, Sheaves of modules and invertible sheaves, differentials
- Sheaf cohomology
- Applications to the study of algebraic curves

Core Documentation

R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977

Reference Bibliography

R. Vakil, Foundations of Algebraic Geometry, available online (https://math.stanford.edu/~vakil/216blog/) U. Gortz, T. Wedhorn: Algebraic Geometry I, Viehweg + Teubner (2010). Q. Liu, Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics, 2006 D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Mathematics, Springer, 2004

Type of delivery of the course

In person lectures by the professor

Type of evaluation

Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list)

teacher profile | teaching materials

Programme

- Introduction and motivation
- Affine and projective schemes, morphisms and properties
- Diviors, Sheaves of modules and invertible sheaves, differentials
- Sheaf cohomology
- Applications to the study of algebraic curves

Core Documentation

R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977

Reference Bibliography

R. Vakil, Foundations of Algebraic Geometry, available online (https://math.stanford.edu/~vakil/216blog/) U. Gortz, T. Wedhorn: Algebraic Geometry I, Viehweg + Teubner (2010). Q. Liu, Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics, 2006 D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Mathematics, Springer, 2004

Type of delivery of the course

In person lectures by the professor

Type of evaluation

Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list)