Printed Matter on Alexei Gorodentsev's ALGEBRAIC GEOMETRY START UP COURSE

You can download at once all available printed matters on this course (they are organized in 74 pages text book) as 791 Kb of gzipped PostScript.

## Approximate program

of this course can be downloaded from here either as zipped PostScript or as gzipped PostScript file.

## Lecture Notes

Here are short notes of some lecture kernels (many actually discussed things are given here only as exercises).

Lecture 1. Projective spaces, projective transformations, and projections.

Lecture 3. Plane drawings: pencils and conics.

Tensor Guide. (Instead of lecture 4)

Lecture 5. Geometry of skew commutative polynomials: Grassmannians.

Lecture 6. Geometry of commutative polynomials: Veronese varieties.

Commutative Algebra Draught. (Instead of lecture 7)

Lecture 8. Projective hypersurfaces (in zero characteristic).

Lecture 9. Plane curves: singularities, intersections, Plücker relations.

Lecture 10. Plane curves: correspondences and Chasles - Cayley - Brill formula.

Lecture 11. Affine Algebraic - Geometric dictionary.

Lecture 12. Algebraic manifolds, morphisms, and the dimension.

Lecture 13. Working example: lines on surfaces.

Lecture 14. Algebraic vector bundles.

Lecture 15. Sheaves.

There are two ways for students to certificate this course. Usually I give 1 or 2 written class tests and a series of home tasks (about 10 sheets with problems published one per week, time to solve them is not restricted). If you either solve about 90% of home tasks or solve about 90% of class tests, then you get the certification for sure. An equivalent intermediate value (say 40% for home + 40% for class) is also enough, certainly. Examples of the home tasks can be downloaded from the list below:

Task 1. Projective spaces, affine charts, coordinates, and projections

Task 3. Plücker -- Segre -- Veronese interaction

Task 4. Some useful (multi) linear algebra

Task 5. Hypersurfaces, tangents, and singularities

## Written Tests

Besides the home tasks, solving the written class tests is the second way to certificate this course. Examples of such the tests can be downloaded from the list below.

Test 1 (on the first part of course).
It was given at Göttingen University, Winter 2002/03

Test 2 (on the second part of course).
It was given at Göttingen University, Winter 2002/03

Test 3 (on a `light version' of this course).
It was given in `Math. in Moscow'
(this is a special program for foreign students
at the Independent University of Moscow), Spring 2002