Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-41-22-M-7

Plane Curve Singularities (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-41-22-M-7 Plane Curve Singularities 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-41-22-K-7
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.


Contents

  • parametrization of plane curves,
  • Puiseux series,
  • Newton polygons,
  • value semigroups,
  • characteristic exponents,
  • resolution of plane curve singularities.

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.

Literature

  • T. De Jong, G. Pfister: Local Analytic Geometry,
  • O. Zariski: The Moduli Problem for Plane Branches, with an appendix by B. Teissier.

References to Module / Module Number [MAT-41-22-M-7]

Module-Pool Name
[MAT-41-MPOOL-7] Specialisation Algebraic Geometry and Computer Algebra (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)