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Algebraic Geometry - Andreas Gathmann

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Andreas Gathmann - Algebraic Geometry (SS 2014)

There are currently two versions of my notes for the Algebraic Geometry class.

Version of 2014

This new version covers the material of one semester, according to our Bachelor course. It has been updated recently, many errors and inconsistencies in the old version below have been fixed, and the exposition has been improved significantly in many places. If possible, you should use this new version. It connects well with our Commutative AlgebraCommutative Algebra class, but no prior knowledge of this class is assumed.

Complete notes (133 pages, 3.1MB, last updated April 18, 2017)
0.Introduction (pdf)
1.Affine Varieties (pdf)
2.The Zariski Topology (pdf)
3.The Sheaf of Regular Functions (pdf)
4.Morphisms (pdf)
5.Varieties (pdf)
6.Projective Varieties I: Topology (pdf)
7.Projective Varieties II: Ringed Spaces (pdf)
8.Grassmannians (pdf)
9.Birational Maps and Blowing Up (pdf)
10.Smooth Varieties (pdf)
11.The 27 Lines on a Smooth Cubic Surface (pdf)
12.Hilbert Polynomials and Bézout's Theorem (pdf)
13.Applications of Bézout's Theorem (pdf)
14.Divisors on Curves (pdf)
15.Elliptic Curves (pdf)

Any comments and corrections welcome!

Version of 2003

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

Complete notes (214 pages, 1.9MB, last updated October 6, 2013)
0. Introduction (pdf)
1. Affine varieties (pdf)
2. Functions, morphisms, and varieties (pdf)
3. Projective varieties (pdf)
4. Dimension (pdf)
5. Schemes (pdf)
6. First applications of scheme theory (pdf)
7. More about sheaves (pdf)
8. Cohomology of sheaves (pdf)
9. Intersection theory (pdf)
10. Chern classes (pdf)