- Docente: Luca Migliorini
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Moduli: Luca Migliorini (Modulo 1) Giovanni Mongardi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
At the end of the course the student: - has a high culture in the geometric, algebraic and differential areas; - is able to use this knowledge in his research in both geometric and algebraic settings.
Course contents
Affine and projective varieties. Zariski topology. Classical examples.The notion of scheme, motivations, examples.The functor of points of a scheme.The spctrum of a commutative ring, the homogeneous spectrum of a graded ring.Some fundamental notions: separatdness and completeness. Morphisms of schemes. Regularity and singularity. Normality. Morphisms of schemes, flatness and smoothness. Quasi coherent and coherent sheaves, and their cohomology. Comparison between schemes opver the complex numbers and analytic spaces.
Readings/Bibliography
Hartshorne algebraic geometry. Liu Algebraic geometry and arithmetic curves. Vakil Foundations of algebraic geometry. Manetti:Geometria algebrica.
Teaching methods
Lectures at the blackboard
Assessment methods
Oral exam
Office hours
See the website of Luca Migliorini
See the website of Giovanni Mongardi