General information |
Course unit name: Local and Global Theory of Algebraic Curves
Course unit code: 364205
Academic year: 2021-2022
Coordinator: Rosa Maria Miro Roig
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time |
Total number of hours 150 |
Face-to-face and/or online activities |
60 |
- Lecture |
Face-to-face |
30 |
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- Lecture with practical component |
Face-to-face |
30 |
Supervised project |
20 |
Independent learning |
70 |
Recommendations |
It is advisable to have basic knowledge of projective geometry and be familiar with the basic concepts of algebra. |
Competences to be gained during study |
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Capacity to study the intrinsic and extrinsic geometry of an algebraic curve. |
Learning objectives |
Referring to knowledge — Acquire basic knowledge of the local, projective and intrinsic theories of algebraic curves.
Referring to abilities, skills — Perform introductory mathematical research in this subject area.
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Teaching blocks |
1. Implicit equations of plane curves; Intersection of plane curves (resultant)
2. Linear systems of curves
3. Parametrisation of curves
4. Local properties of curves
5. Bézout’s theorem and its applications
6. Plücker formulas; Applications
7. Rational curves; Curves of small genus
8. Higher-dimensional varieties
Teaching methods and general organization |
• In the expected blended teaching model:
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Official assessment of learning outcomes |
Continuous assessment consists of:
Examination-based assessment Students following single assessment take an examination on the whole contents of the subject, on the same date as the final examination for continuous assessment. This option must be requested of the Secretary’s Office at the Faculty before the established date. The mark obtained in this examination is the final grade for the subject.
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Reading and study resources |
Consulteu la disponibilitat a CERCABIB
Book
M. Reid, Undergraduate Algebraic Geometry, LMS Students Texts 12, Cambridge Univ. Press, 1988
R.J. Walker, Algebraic curves, Springer-Verlag, 1978
K. Hulek, Elementary Algebraic Geometry, Student Mathematical Library AMS
Volume: 20; 2003;