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This is intended to be a "second course" in algebraic geometry. Using vector bundles on projective spaces as the driving set of examples, we will see how various methods of algebraic geometry are applied in practice.
Preliminary program
- Vector bundles and coherent sheaves
- Cohomology of coherent sheaves and basic theorems
- Chern classes
- Grothendieck's theorem, jump lines, Horrocks criterion
- Bundles with different properties: uniform bundles, Tango example, Serre construction
- Topological classification
- Stability in the sense of Mumford and Gieseker
- Splitting of stable bundles
- Beilinson's theorem
- Moduli spaces
 RSS: Forthcoming seminars
 Lecturer
Fonarev Anton Vyacheslavovich
Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
