27th Autumn School in Algebraic Geometry

Algebraic geometry and derived categories

Lukecin, Poland, September 19th - September 25th, 2004

Teachers: Andrei Caldararu (Philadelphia, US) and Miles Reid (Warwick, UK)

Program: An introduction to algebraic geometry featuring derived categories and some of their applications.

Plan of Caldararu's lectures:

  1. The derived category.
  2. Triangles, exactness and derived functors.
  3. The derived category of P^n amd orthogonal decomposition.
  4. Serre duality and apleness of canonical class.
  5. Moduli problems and equivalences.
  6. Hochschild homology and cohomology.
Notes to Caldararu's lectures

Plan of Reid's lectures:

  1. Nontechnical introduction to derived categories and comparison with cohomology theories.
  2. The McKay correspondence as an application of Fourier-Mukai transforms.
  3. Calculation of Hilbert schemes for Abelian and almost Abelian groups in SL(2,C) and SL(3,C).
  4. Graded rings and algebraic varieties.
Readings to Reid's lectures:
  • Reid, Chapters on algebraic surfaces, IAS/Park City lecture notes series, 1993.
  • Reid, More chapters: Cyclic quotient singularities, Graded rings and homework to these chapters.

    Additional talks:

    1. Introduction to abelian category, by Baire Cooper.
    2. Introduction to triangulated category, by Baire Cooper.
    3. How to use Beilinson spectral sequence, by Daniele Faenzi.
    4. Resolution of quotient terminal singularities and McKay correspondence, by Oskar Kedzierski.

    Organizers: Jaroslaw Buczynski and Jaroslaw Wisniewski.

  • Joint picture of all participants
  • September Schools Homepage
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