Algebraic Geometry (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||9.0 CP||186 h|
|2||U||Exercise class (in small groups)||28 h|
|(4V+2U)||9.0 CP||84 h||186 h|
- 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:
- differential forms,
- further aspects of Algebraic Geometry.
- 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.
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.
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-40-11-M-4] Commutative Algebra (M, 9.0 LP)
Requirements for attendance (formal)
References to Course [MAT-40-12-K-7]
|[MAT-40-12-M-7]||Algebraic Geometry||P: Obligatory||4V+2U, 9.0 LP|