Viktor Levandovskyy WS 2016-2017 Algebraic Geometry
(For) Students

Algebraic Geometry

PD Dr. Viktor Levandovskyy

The link to the computer algebra system SINGULAR: and its online interface.
The link to the free visualization tool surfer.

Actual Information

Changes: after Halloween, lectures on Thu and Fri in SeMath will be in the timeslot 8:30 - 9:55.
from 24 Oct on, example classes will take place on Fri 12:15 in Seminarraum LDfM (Pontdriesch 14-16).

Please register in the L2P space for the lecture.
Lecture notes are available there, I plan to make assignments there as well.

Example class assignment for Fri 16 Dec: 8.2, 8.9, 8.12, 8.19, 8.21
Example class assignment for Thu 22 Dec: 9.2', 9.2'', 9.5, 9.6; think about Thm 9.8 and its subitems

General Information

Lectures and example classes will take place mostly before Christmas with possible augmentation in the 2017.

Prerequisites: Linear Algebra I and II, Computer Algebra

Wed, 14:15 - 15:45 (HS IV)
Thu, 08:30 - 09:55 (SeMath, Pontdriesch 14-16)
Fri, 08:30 - 09:55 (SeMath, Pontdriesch 14-16)
Example classes:
Fri, 12:15 - 13:45 (Seminarraum LDfM, Pontdriesch 14-16)

Algebraic sets, ideals, varieties and operations with them.
Affine and projective varieties. Hilbert's Nullstellensatz.
Morphisms between varieties, product of varieties. Dictionary between algebra and geometry.
Integral extensions and Noether normalization. Dimension theory (Krull, transcendence degree).
Solving systems of polynomial equations. Introduction to sheaves.
Abstract algebraic varieties, separated, complete and normal varieties.

RWTH Aachen University Division of Mathematics Lehrstuhl B für Mathematik