Intensive course by E. Arbarello / Fall 2019

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
HSE University, Faculty of Mathematics, 6 Usacheva str.,

= = = on Tuesdays, 17:00 – 19:00, room 213, and
= = = on Thursdays, 16:00 – 18:00, room 110.

Starting Tuesday, September 24th, 2019

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)

This lecture series is made possible by the support of the Skolkovo Institute of Science and Technology