Introduce to the study of algebraic geometry, with particular emphasis on beams, schemes and cohomology.
Curriculum
scheda docente
materiale didattico
- Affine and projective schemes, morphisms and properties
- Diviors, Sheaves of modules and invertible sheaves, differentials
- Sheaf cohomology
- Applications to the study of algebraic curves
Programma
- 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
Testi Adottati
R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977Bibliografia Di Riferimento
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, 2004Modalità Erogazione
In person lectures by the professorModalità Valutazione
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)
scheda docente
materiale didattico
- Affine and projective schemes, morphisms and properties
- Diviors, Sheaves of modules and invertible sheaves, differentials
- Sheaf cohomology
- Applications to the study of algebraic curves
Programma
- 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
Testi Adottati
R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977Bibliografia Di Riferimento
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, 2004Modalità Erogazione
In person lectures by the professorModalità Valutazione
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)