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