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ФКН

Enrico Arbarello (Sapienza Università di Roma) : "Bridgeland theory and its applications in algebraic geometry"

September 24 to November 21, 2019 Enrico Arbarello (Sapienza Università di Roma) gives an intensive course "Bridgeland theory and its applications in algebraic geometry".Lectures take place at the Faculty of Mathematics, ul. Usacheva d. 6, on Tuesdays, 17:00 - 19:00, room 213, and on Thursdays, 16:00 - 18:00, room 110. The first lecture will be on Tuesday, September 24th.

COURSE DESCRIPTION:
The aim of the course is to give an introduction to Bridgeland theory together with various application of this theory to classical algebraic geometry: Brill-Noether Theory, curves on K3 surfaces, etc.
We give give a bird-eye view on these subjects, providing proofs only here and there but giving many examples.

PREREQUISITES: Basic algebraic geometry, including schemes and sheaves (covered by Hartshorne and Schafarevich textbooks) and basic homological algebra, including derived categories and cohomologies of sheaves (covered by Gelfand-Manin).

COURSE PROGRAM:
Quot schemes and moduli (6 lectures)
Classical algebraic geometry (5 or 6 lectures):
    - Brill-Noether theory
    - K3 surfaces
Bridgeland theory and applications (5 or 4 lectures)