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Algebraic Geometry

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Algebraic Geometry

Lecturer:

Prof. Dr. Wolfram Decker


Assistant:

Isabel Stenger


Dates:

Lectures: Tuesday 10:00-11:30 Room 48-438
Thursday 10:00-11:30 Room 48-438
Exercise Class: Friday 11:45-13:15 Room 48-438

News:

Please register for the exercise class through the online system URM by October 28th.


Content:

Affine and projective varieties.
Morphisms, dimension and singularities.
Sheaves and cohomology of sheaves.
Divisors and the Riemann-Roch theorem.
Applications of the Riemann-Roch theorem.

Homework

There will be weekly homework assignments posted on this page, typically posted on Tuesday and due on the next Tuesday by 10:00 am. You may turn in your homework in groups of up to 3 persons.

Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
Sheet 8
Sheet 9
Sheet 10
Sheet 11
Sheet 12
Sheet 13

Pictures:

Blowing-up

Choncoid of Nicomedes

Projective Space

Surfaces

Projection


Credit Points:

Regular, active and successful participation in the exercise classes is required to achieve an "Übungsschein". This includes scoring at least 40% of the exercise points and presenting own solutions on the black board.

You have to pass an oral exam at the end of the term in order to get credit points for this lecture.


Literature:

D. A. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms.
W. Decker, G. Pfister, A First Course in Computational Algebraic Geometry.
W. Decker, F.-O. Schreyer, Varieties, Groebner Bases, and Algebraic Curves.
D. Eisenbud and J. Harris, The Geometry of Schemes.
R. Hartshorne, Algebraic Geometry.
Q. Liu, Algebraic Geometry and Arithmetic Curves.
M. Reid, Undergraduate Algebraic Geometry .
I. Shafarevich, Basic Algebraic Geometry 1/2.