Unit ALGEBRICAL GEOMETRY
- Course
- Mathematics
- Study-unit Code
- 55A00107
- Curriculum
- Didattico-generale
- Teacher
- Daniele Bartoli
- Teachers
-
- Daniele Bartoli
- Massimo Giulietti (Codocenza)
- Hours
- 42 ore - Daniele Bartoli
- 21 ore (Codocenza) - Massimo Giulietti
- CFU
- 9
- Course Regulation
- Coorte 2024
- Offered
- 2025/26
- Learning activities
- Caratterizzante
- Area
- Formazione teorica avanzata
- Academic discipline
- MAT/03
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Review of Algebraic and Projective Varieties. Sheaves, Ringed Spaces, Schemes. Algebraic curves.
- Reference texts
- J. Bochnak, M. Coste, M. F. Roy, Real algebraic geometry. Springer 1998
D. Munford, The red book of varieties and schemes. Springer 1988
I. R. Shafarevich, Basic Algebraic Geometry. Springer 1974
Further notes and references will be supplied by the lecturer - Educational objectives
- The course introduces to the theory of algebraic varieties as ringed spaces. Its goal is to familiarize the students with the tools they will need in order to use algebraic varieties, also with regard to other fields of the geometry. A specific part will be dedicated to algebraic curves in arbitrary characteristic
- Prerequisites
- Elements of linear algebra, commutative algebra and fields theory, wich are stated as needed, and some elementary topology. Finite group theory.
- Teaching methods
- Face-to-face lecture, office hours, usually after the lectures, or by appointment, usage of the platform Teams.
- Other information
- For other information pleas contact the teachers of the course: daniele.bartoli@unipg.it massimo.giulietti@unipg.it For information of DSA students please visit http://www.unipg.it/disabilita-e-dsa
- Learning verification modality
- The final exam consists in an oral discussion of about an hour on the subjects developped during the course. A detailed list of the subjects is provided at the end of the lectures. The aim of the exam is to evaluate the level and the quality of the knowledge the students have acquired
and to check their ability in the exposition. - Extended program
- Review of Algebraic and Projective Varieties. Sheaves, Ringed Spaces, Schemes. Algebraic curves. Riemann and Riemann-Roch Theorems. Coverings of curves. Automorphisms of curves.
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- 4