Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mccme.ru/mathinmoscow/listcur/Algebraic%20Geometry.htm Дата изменения: Sun Jul 28 22:08:52 2013 Дата индексирования: Fri Feb 28 00:14:35 2014 Кодировка:

J. Harris, Algebraic Geometry. A First Course., Springer.

M. Reid, Undergraduate algebraic geometry, Cambridge: Cambridge Univ. Press, 1988. "; $programm = "

Projective spaces.

Projective conics and PGL(2)

Geometry of projective quadrics. Spaces of quadrics

Grassmannians.

Examples of projective maps: Pluecker, Segre, Veronese.

Integer ring extensions, polynomial ideals, affine algebraic geometry and Hilbert's theorems.

Algebraic varieties, Zarisky topology, schemes, geometry of ring homomorphisms.

Irreducible varieties. Dimension.

Plane projective algebraic curves: point multiplicities, intersection numbers, Bezout's theorem.

Plane projective algebraic curves: singularities, duality, Pluecker formulas.

Rational curves. Veronese curve. Cubic curves.

Curves on surfaces. The 27 lines on a smooth cubic surface.

Vector bundles and their section sheaves. Vector bundles on the projective line.

Linear systems and invertible sheaves, the Picard group, line bundles on affine and projective spaces.

Tangent, cotangent, normal and conormal bundles. The Euler exact sequence.

Singularities and tangent cone. Blow up.

Complex projective curves: canonical class, genus, Serre duality and Riemann-Roch theorem.

If time allows: Ponselet's porism; quadrics through a canonical curve; Klebsh and Luroth problems, and so on. "; ?>