A.Gorodentsev

Algebraic geometry: a start-up course

This is not an IUM course; what follows is lecture notes (in English) of the course given by our professor Alexey Gorodentsev at the University of Warwick (UK) in the Spring semester of 1999.

Lecture notes in English

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

[Lecture 1 (67K)|Lecture 2 (77K)|Lecture 3 (91K)|Lecture 4 (80K)
Lecture 5 (111K)|Lecture 6 (177K)|Lecture 7 (75K)|Lecture 8 (131K)
Lecture 9 (80K)|Lecture 10 (94K)|Lecture 11 (94K)|Lecture 12 (83K)
Lecture 13 (77K)|Lecture 14 (75K)|Lecture 15 (98K)|Lecture 16 (95K)
Lecture 17 (104K)|Lecture 18 (103K)|Lecture 19 (106K)|Lecture 20 (155K)
Lecture 21 (86K)|Lecture 22 (94K)|Lecture 23 (94K)|Lecture 24 (92K)]

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[Lecture 1 (27K)|Lecture 2 (31K)|Lecture 3 (36K)|Lecture 4 (32K)
Lecture 5 (41K)|Lecture 6 (60K)|Lecture 7 (30K)|Lecture 8 (50K)
Lecture 9 (32K)|Lecture 10 (36K)|Lecture 11 (38K)|Lecture 12 (33K)
Lecture 13 (32K)|Lecture 14 (31K)|Lecture 15 (38K)|Lecture 16 (38K)
Lecture 17 (41K)|Lecture 18 (40K)|Lecture 19 (41K)|Lecture 20 (53K)
Lecture 21 (34K)|Lecture 22 (37K)|Lecture 23 (38K)|Lecture 24 (36K)]

Syllabus

  1. Polynomial algebra, affine space, and projective space associated with a given vector space.
  2. Projective spaces: coordinates, affine covering, and subspaces.
  3. Projective spaces: projections and line projective isomorphisms.
  4. Projective quadrics: the basics.
  5. Projective quadrics: complex plane conics.
  6. Projective quadrics: some drawings.
  7. Projective quadrics: linear subspaces on a non singular quadric, Segre.
  8. Tensor guide (instead of lecture 8).
  9. Grassmannian polynomials: computation examples.
  10. G(2,4) and 3D line geometry.
  11. Grassmannians in general.
  12. Contractions and polarizations.
  13. Linear span of a tensor. Plücker relations.
  14. Partial derivatives and Veronese varieties.
  15. Geometry of Veronese curve.
  16. Projective hypersurfaces.
  17. Plane curves: intersections.
  18. Plane curves: singular points and tangents.
  19. Plane curves: Plücker formulas and duality.
  20. Plane curves: Chasles - Cayley - Brill formula.
  21. Commutative algebra draught.
  22. Algebraic - geometric dictionary.
  23. Algebraic manifolds.
  24. Some morphisms.
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