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Quiver varieties

External Lecturer: 
Claudio Bartocci
Course Type: 
PhD Course
Anno (LM): 
First Year
Academic Year: 
20 h


  • Basic definitions
  • Gabriel’s theorem
  • Double quivers
  • Quiver representations
  • Quiver varieties
  • Hilbert schemes of points on complex surfaces as quiver varieties
  • The ADHM description of the moduli space of instantons on R4
  • Instantons on ALE spaces and the geometric McKay correspondence

Basic references

  • C. Bartocci, V. Lanza, C.L.S. Rava, “Moduli spaces of framed sheaves and quiver varieties”, Journal of Geometry and Physics 118 (2017), 20–39.
  • C. Bartocci, U. Bruzzo, V. Lanza, C.L.S. Rava, “On the irreducibility of some quiver varieties”, SIGMA 16 (2020), 13 pages.
  • A. Kirillov Jr., Quiver Representations and Quiver Varieties, AMS, Providence (RI) 2016.
  • H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, AMS, Providence (RI) 1999.
  • O. Schiffmann, “Variétés carquois de Nakajima”, in: Séminaire Bourbaki 2006/2007 – Exposés 967–981, Astérisque 311 (2008), 295–344.
Next Lectures: 

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