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MAI0128 Programme and Aims
Aims
The course is an introduction to algebraic geometry. In the course we will treat the basic concepts in algebraic geometr, with a final application to complex curves. The first lecture will study curves as first examples of algebraic varieties.Contents
- Projective and affine planes, (homogeneous) coordinates, curves and their genus.
- Affine varieties, affine subvarieties, Zariski topology, ideals of affine subvarieties. Coordinate rings, isomorphisms, rational maps.
- Projective varieties and subvarieties, products, regular maps, birational equivalence.
- Ramification, elliptic curves.
- coverings of curves,the Riemann-Roch Theorem.
Sidansvarig: milagros.izquierdo@liu.se
Senast uppdaterad: 2019-11-29