- parametrization of plane curves,
- Puiseux series,
- Newton polygons,
- value semigroups,
- characteristic exponents,
- resolution of plane curve singularities.
Plane Curve Singularities (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-41-22-M-7||Plane Curve Singularities||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.
Plane Curve Singularities
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-41-22-K-7]: Title: "Plane Curve Singularities"; 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: 86356 ("Plane Curve Singularities")
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 and understand the basic methods and statements for the study of plane curve singularities. They thereby have become acquainted with important invariants and they are able to investigate them using scientific methods. They can name the essential propositions of the lecture as well as classify and explain the presented connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can outline the conditions and assumptions that are necessary for the validity of the statements.
By working on exercises, they have acquired a safe, precise and independent handling of the terms, statements and methods from the lecture.
- T. De Jong, G. Pfister: Local Analytic Geometry,
- O. Zariski: The Moduli Problem for Plane Branches, with an appendix by B. Teissier.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-40-11-M-4] Commutative Algebra (M, 9.0 LP)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-24-K-3] Introduction to Complex Analysis (2V+1U, 4.5 LP)
Requirements for attendance (formal)