Content

Algebraic geometry is concerned with the study of solutions of polynomial equations. As opposed to what you know from linear algebra, such solutions can not be obtained explicitly in general. Instead, algebraic geometry provides an abstract language and tools to understand polynomial equations from a qualitative point of view, e.g. to make sense of the dimension of the solution space. These methods are based on the interplay of (commutative) algebra and geometry/topology. The main objects of interest are so-called varieties or, more generally, schemes. These are are equipped with the so-called Zariski topology and a structure sheaf which encodes the algebraic information of a system of polynomial equations. The course is an introduction to the basic concepts of algebraic geometry covering varieties and morphisms, projective varieties, dimension, and schemes.

Tutorial

The tutorial will be held by Cornelia Rottner. If you wish to attend, please enroll via URM by April 19, 2013.

Homework

There will be weekly homework assignments posted on this page. Typically assignment will be posted on Friday, and due on the following Friday by 3:00pm. Please drop your solutions by the respective due date in the mail box of Cornelia Rottner next to room 48-210. You may (and you are encouraged to) turn in your homework in teams of 3. However, each of you needs to be able to present your team's solutions during the tutorial.

	Assignment 1 (due April 26, 2013, 1:00 pm)
	Assignment 2 (due May 3, 2013, 1:00 pm)
	Assignment 3 (due May 10, 2013, 1:00 pm)
	Assignment 4 (due May 17, 2013, 1:00 pm)
	Assignment 5 (due May 24, 2013, 1:00 pm)
	Assignment 6 (due May 31, 2013, 1:00 pm)
	Assignment 7 (due June 7, 2013, 1:00 pm)
	Assignment 8 (due June 14, 2013, 1:00 pm)
	Assignment 9 (due June 21, 2013, 1:00 pm)
	Assignment 10 (due June 28, 2013, 1:00 pm)
	Assignment 11 (due July 5, 2013, 1:00 pm)
	Assignment 12 (due July 12, 2013, 1:00 pm)

Credit

In order to obtain an Übungsschein you need to actively participate in the tutorial and achieve a total homework score of at least 40%. Active participation means regular attendance and presenting a solution of a homework problem (at least once).

For credit points you need to pass an oral exam after the end of the semester.

Literature

	Andreas Gathmann: Algebraic Geometry, Chapters 1-6.
	For secondary literature, see the last page of above script.