Department of Mathematics
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Class Notes

Andreas Gathmann

Class Notes Algebraic Geometry

As the syllabus of our Algebraic Geometry class seems to change every couple of years, there are currently three versions of my notes for this class.

Version of 2021/22

This is the current version of the notes, corresponding to our Algebraic Geometry Master course. It has been updated recently, many errors and inconsistencies in the old versions below have been fixed, and the exposition has been improved significantly in many places. If possible, you should use this new version. It assumes the material of our Commutative Algebra Bachelor class – not very much at the beginning, but more and more so towards the end (so taking both classes in the same semester may be possible). Prior knowledge of our Plane Algebraic Curves Bachelor class is not required, but certainly useful as it gives a more gentle introduction to the field of algebraic geometry – in particular since material specific to (plane) curves has deliberately been left out here in order to avoid significant intersections of the two classes.

Any comments or corrections are welcome!

Version of 2014

This version used to be a Bachelor course some time ago. It can be used as an introduction to algebraic geometry with almost no prerequisites – it connects well with our Commutative Algebra course, but no prior knowledge of this class is assumed. It does not mix very well with our Plane Algebraic Curves class however: the latter did not exist at the time of writing these notes, so there is a substantial amount of overlap.

Version of 2002/03

This is the original version of the class notes, which will not be updated any more. However, it covers two semesters, and thus contains more material than the new versions above.