Derived categories of hypersurfaces (Selected Topics in Algebraic Geometry, V5A4 Summer 2018)


Prerequisites: Hartshorne Chapters II+III. Certain things will have to be accepted as black-boxes, e.g. Serre duality, technical details of derived categories, derived functors,...

Topics (subject to changes)


    1. April 11: Quick Introduction: Derived categories,

    2. April 18: Derived functors, Serre duality, Grothendieck-Ver\ dier duality, Fourier-Mukai formalism. (Essentially no proofs, depending on the audience.)

    3. April 25: Theorem of Bondal-Orlov: Varieties with ample (anti-)canonical bundle are determined by their deriv\ ed category Semi-orthogonal decompositions, exceptional collections

    4. May 9: Semi-orthogonal decompositions, exceptional collections

    5. June 6: Kuznetsov's category, fractional CY categories Categories of graded matrix factorizations (Orlov's description of Kuznetsov's category)

    6. June 13: Categories of graded matrix factorizations (Orlov's description of Kuznetsov's category)

    7. June 20:

    8. July 4:

    9. July 11:

References:
  • D. Huybrechts: Fourier-Mukai transforms in algebraic geometry. Oxford Mathematical Monographs. 2006.

  • C. Weibel: An Introduction to Homological Algebra. Cambridge. 1994

  • tbc