Teaching plan for the course unit

 

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General information

 

Course unit name: Algebraic Curves

Course unit code: 568188

Academic year: 2018-2019

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 learning activities

60

 

-  Lecture

 

30

 

-  Lecture with practical component

 

30

Supervised project

(Problem-solving exercises and preparation of assignments.)

20

Independent learning

(Theory study, preparation of project presentations and the final exam.)

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

 


— Capacity to study the intrinsic and extrinsic geometry of an algebraic curve.

 

 

 

 

Learning objectives

 

Referring to knowledge


— To acquire basic knowledge of the local, projective and intrinsic theories of algebraic curves.

 

Referring to abilities, skills


— To perform introductory mathematical research in this subject area.
— To utilise basic bibliographic reference material on the subject.

 

 

Teaching blocks

 

1. Implicit equations of plane curves. Intersection of plane curves (Resultant)

2. Linear systems of curves

3. Parametrization of curves

4. Local study of curves

5. Bezout’s theorem and applications

6. Pücker formulas. Applications

7. Rational curves. Curves of small genus.

8. Varieties of higher dimension

 

 

Teaching methods and general organization

 


The teaching methodology for the subject includes:

• Two hours of lecture classes devoted to theory per week;
• Two hours of practical classes devoted to problem-solving exercises per week;
• A tutored personal project structured around problem-solving exercises and the preparation of assignments;
• Independent learning.
 
In lectures the teacher provides the main definitions and results relevant to the subject, and illustrates them with examples. Lists of exercises for each topic are also handed out, and students are required to present their solutions on the board in class. Throughout the semester each student is assigned a personal project related to the course content, to be presented to the class at a time during the course or in dedicated sessions that take place once the face-to-face lectures have all been completed.

 

 

 

Official assessment of learning outcomes

 


Grades are awarded based on participation in practical classes and the preparation and presentation of assignments. In cases where a pass grade is not achieved or a student wishes to improve their score, a final examination must be completed.

 

Examination-based assessment


For students who opt out of continuous assessment (problem-solving exercises and assignments), a final examination must be completed.

 

 

Reading and study resources

Consulteu la disponibilitat a CERCABIB

Book

Fulton, W. Curvas algebraicas : introducción a la geometrķa algebraica. Barcelona [etc.] : Reverté, 2005.  EnllaƧ

Fisher, G. Plane algebraic curves. [Providence (R.I.)] : American Mathematical Society, 2001.  EnllaƧ

Griffiths, P. Introduction to algebraic curves. Providence (R.I.) : American Mathematical Society, 1989.  EnllaƧ

Miranda, R. ALgebraic curves and Riemann surfaces, Graduate Studies in Mathematics. Providence (R.I.) : American Mathematical Society, 1995.  EnllaƧ

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;

Web page

E. Arrondo, Curvas Algebraicas, Notas curso 2017.