ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Provide the students a basic introduction to Algebraic Geometry over algebraically closed fields.
Affine algebraic sets. Affine varieties. The n-dimensional projective space. Projective algebraic sets. Projective varieties. (3 hours)
Regular functions. The local ring of a point. The rational function field. Morphisms of varieties. Rational maps. Birational equivalence. (7 hours)
Nonsingular varieties. Nonsingular points and regular local rings. Blowing-ups. Dimension. Divisors. Intersections in the affine and projective spaces. Intersection with hypersurfaces. Nonsingular curves. Plane curves. Riemann.Roch theorem for nonsingular plane curves. (10 hours)
Introduction to the theory of schemes. (2 hours)
Hartshorne, R.: Algebraic Geometry, Graduate Texts in Math. 52, Springer–Verlag, Heidelberg, 1977.
Also:
Bump, Daniel.: Algebraic geometry, World Scientific Publishing, 1998.
Mumford, D.: Algebraic geometry. I. Complex projective varieties, Springer, 1976.
Mumford, D.; Oda, T. Algebraic Geometry II, Hindustan Book Agency, 2015.
Shafarevich, I. R.: Basic Algebraic Geometry I. Varieties in Projective Space, Springer–Verlag, Heidelberg, 1994.
CG01 - Introduce students into the research, as an integral part of a deep formation, preparing them for the eventual completion of a doctoral thesis.
CG02 - Acquisition of high level mathematical tools for diverse applications covering the expectations of graduates in mathematics and other basic sciences.
CG03 - Know the broad panorama of current mathematics, both in its lines of research, as well as in methodologies, resources and problems it addresses in various fields
CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context
CB10 - That students have the learning skills that allow them to continue studying in a way that will be largely self-directed or autonomous.
CE01 - Train for the study and research in mathematical theories in development.
Both, teacher and students, will lecture.
Maximum of the score of students' talks (if any) and the final exam, in any of the three settings.
It depends on the student.
Basic knowledge of Commutative Algebra is necessary, such as the one provided by the subject "Algebra Conmutativa" in this master.
Teaching methodology. Both, teacher and students, will lecture. In the second scenario, there can be in-person and online classes, while in the third one one only online classes.
Assessment system. Maximum of the score of students' talks (if any) and the final exam, in any of the three scenarios.
José Javier Majadas Soto
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813168
- j.majadas [at] usc.es
- Category
- Professor: University Professor
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Classroom 10 |
| 12:00-13:00 | Grupo /CLIL_01 | Spanish | Classroom 10 |