27th Autumn School in Algebraic Geometry
Algebraic geometry and derived categories
Lukecin, Poland, September 19th - September 25th, 2004
Andrei Caldararu (Philadelphia, US) and Miles Reid (Warwick, UK)
An introduction to algebraic geometry featuring derived categories
and some of their applications.
Plan of Caldararu's lectures:
Notes to Caldararu's lectures
- The derived category.
- Triangles, exactness and derived functors.
- The derived category of P^n amd orthogonal decomposition.
- Serre duality and apleness of canonical class.
- Moduli problems and equivalences.
- Hochschild homology and cohomology.
Plan of Reid's lectures:
Readings to Reid's lectures:
on algebraic surfaces, IAS/Park City lecture notes series,
Reid, More chapters: Cyclic
quotient singularities, Graded
rings and homework to
- Nontechnical introduction to derived
categories and comparison with cohomology theories.
McKay correspondence as an application of Fourier-Mukai
- Calculation of Hilbert schemes for Abelian and almost
Abelian groups in SL(2,C) and SL(3,C).
- Graded rings and algebraic
- Introduction to abelian category, by Baire Cooper.
- Introduction to triangulated category, by Baire Cooper.
- How to use Beilinson spectral sequence, by Daniele Faenzi.
- Resolution of quotient terminal singularities and McKay correspondence, by
Organizers: Jaroslaw Buczynski and Jaroslaw Wisniewski.
Joint picture of all participants