Module Handbook

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Course MAT-40-12-K-7

Algebraic Geometry (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [7] Master (Advanced)
Language [EN] English
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

Compulsory Topics:
  • affine and projective varieties (especially: dimension, morphisms, smooth and singular points, blow-ups of points, applications and examples),
  • sheaves and sheaf cohomology with applications (Riemann-Roch Theorem for curves, projective embedding of a curve).

In addition, a selection of the following topics is covered:

  • schemes,
  • differential forms,
  • further aspects of Algebraic Geometry.

Literature

  • D. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms,
  • I. Dolgachev: Introduction to Algebraic Geometry,
  • J. Harris: Algebraic Geometry,
  • R. Hartshorne: Algebraic Geometry,
  • D. Mumford: The Red Book of Varieties and Schemes,
  • H.A. Nielsen, Algebraic Varieties,
  • M. Reid: Undergraduate Algebraic Geometry,
  • I. R. Shafarevich: Basic Algebraic Geometry 1: Varieties in Projective Space.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Requirements for attendance (informal)

Knowledge from the course [MAT-40-28-K-4] is useful but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-40-12-K-7]

Module Name Context
[MAT-40-12-M-7] Algebraic Geometry P: Obligatory 4V+2U, 9.0 LP