Algebraic geometry III - selected topics
MATH-535
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Summary
This course is an introduction to the theory of algebraic curves and surfaces. An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foundation for further study.
Content
- Recap: Divisors, sheaf cohomology and morphisms to projective spaces
- Riemann-Roch and Serre duality for curves
- Riemann-Hurwitz
- Classification of curves
- Embedding of curves in projective spaces
- Algebraic surfaces
- Intersection theory on smooth surfaces
- Blow-ups
- Fibrations of surfaces
