- singularities of plane curves, Puiseux series,
- projective curves in n-dimensional space, Castelnuovo's inequality,
- classification of curves and moduli spaces,
- Jacobian variety, Abel’s Theorem.
Curves in Projective Space (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-41-21-M-7||Curves in Projective Space||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Curves in Projective Space
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-41-21-K-7]: Title: "Curves in Projective Space"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86187 ("Curves in Projective Space")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of this module, the students have learnt the central concepts, results and methods of a selected branch of algebraic geometry. They have thereby developed a deeper understanding of algebraic curves and of their classification.They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they can critically assess the conditions and assumptions that are necessary for the validity of the statements. Moreover they can apply the techniques of the proofs to other questions in algebraic geometry.
- R. Miranda: Algebraic curves and Riemann surfaces,
- F. Kirwan: Complex algebraic curves,
- W. Fulton: Algebraic curves.
Requirements for attendance (informal)
Requirements for attendance (formal)