Algebraic Geometry (Spring 2003)

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

Contents:
program lecture notes home tasks written tests exercise sheets (in Russian)

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.
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Lecture 2. Projective quadrics.
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Lecture 3. Plane drawings: pencils and conics.
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Tensor Guide. (Instead of lecture 4)
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Lecture 5. Geometry of skew commutative polynomials: Grassmannians.
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Lecture 6. Geometry of commutative polynomials: Veronese varieties.
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Commutative Algebra Draught. (Instead of lecture 7)
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Lecture 8. Projective hypersurfaces (in zero characteristic).
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Lecture 9. Plane curves: singularities, intersections, Plücker relations.
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Lecture 10. Plane curves: correspondences and Chasles - Cayley - Brill formula.
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Lecture 11. Affine Algebraic - Geometric dictionary.
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Lecture 12. Algebraic manifolds, morphisms, and the dimension.
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Lecture 13. Working example: lines on surfaces.
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Lecture 14. Algebraic vector bundles.
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Lecture 15. Sheaves.
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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
You can download either zipped PostScript or gzipped PostScript file.

Task 2. Projective quadrics, especially conics
You can download either zipped PostScript or gzipped PostScript file.

Task 3. Plücker -- Segre -- Veronese interaction
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Task 4. Some useful (multi) linear algebra
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Task 5. Hypersurfaces, tangents, and singularities
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Task 6. Polynomial ideals
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Task 7. Plane curves.
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Task 8. Algebraic manifolds backgrounds.
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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
You can download either zipped PostScript or gzipped PostScript file.

Test 2 (on the second part of course).
It was given at Göttingen University, Winter 2002/03
You can download either zipped PostScript or gzipped PostScript file.

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
         You can download either zipped PostScript or gzipped PostScript file.

Test 4 (on a preliminary version of this course).
It was given at Warwick University, Spring 1999
You can download either zipped PostScript or gzipped PostScript file.

Exercise sheets (in Russian)

Approximate program

Lecture Notes

Home Tasks

Written Tests

Gzipped postscript (may be viewed directly by some versions of ghostview)

Zipped postscript

Exam (in Russian)