Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-42-22-M-7

Complex Manifolds and Hodge Theory (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-42-22-M-7 Complex Manifolds and Hodge Theory 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-42-22-K-7
Complex Manifolds and Hodge Theory
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-42-22-K-7]: Title: "Complex Manifolds and Hodge Theory"; 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: 86157 ("Complex Manifolds and Hodge Theory")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • complex manifolds, subvarieties,
  • vector bundles, sections, cohomology,
  • applications, e.g. divisors and line bundles,
  • differential forms,
  • Serre duality.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the basic definitions, constructions and propositions in the theory of complex manifolds and Hodge theory. They have studied important examples of complex manifolds and are able to analyse them with scientific methods. 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.

Literature

  • P. Griffiths, J. Harris: Principles of Algebraic Geometry,
  • K. Fritzsche, H. Grauert: From Holomorphic Functions to Complex Manifolds.

References to Module / Module Number [MAT-42-22-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.)