## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-40-12-K-7

## 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 9.0 CP = 270 h 1 Sem. in WiSe [7] Master (Advanced) [EN] English Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Schulze, Mathias, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [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.

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