Seminar: Donaldson-Thomas theory, Fall 2021, Georg Oberdieck

Date: Friday 12-2pm (!), Endenicher Allee 60, N 0.003 - Neubau (the small separate building in the back)

First day of class: October 22nd.

The seminar will concern the construction and basic methods of Donaldson-Thomas theory, by which we mean the intersection theory of the moduli spaces of sheaves on smooth projective threefolds. We first focus on the construction of the virtual fundamental class using results of Huybrechts-Thomas, and then discuss localization techniques, in particular the Graber-Pandharipande virtual localization, and how to apply them to local surfaces, local curves, etc. The variant of Pandharipande-Thomas theory will be also discussed.

Prerequisites: Algebraic Geometry I/II (schemes and cohomology), Intersection theory (Fulton's book), Derived categories.

If you are interested to partipate, send me an email or come to the first meeting. The precise schedule will be finalized around the the of the first meeting.

Files for the seminar:

  1. Schedule (preliminary)
  2. Notes Talk 1
  3. Notes Talk 2
  4. Notes Talk 3
  5. Notes Talk 4
  6. Notes Talk 5
  7. Notes Talk 6
  8. Notes Talk 7
  9. Notes Talk 8
  10. Notes Talk 9
  11. Notes Talk 10