On the Kummer construction for Kcsc metrics

  • Claudio ArezzoEmail author
  • Alberto Della Vedova
  • Riccardo Lena
  • Lorenzo Mazzieri


Given a compact constant scalar curvature Kähler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kähler Ricci-flat resolution, we find sufficient conditions on the position of the singular points to ensure the existence of a global constant scalar curvature Kähler desingularization. We also give complete proofs of a number of analytic results which have been used in this context by various authors. A series of explicit examples is discussed.

Mathematics Subject Classification

58E11 32C17 



We wish to express our deep gratitude to Gavin Brown and Alexander Kasprzyk for their help in not drowning in the Fano toric threefolds world. The authors have been partially supported by the FIRB Project “Geometria Differenziale Complessa e Dinamica Olomorfa”.


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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.ICTP TriesteTriesteItaly
  2. 2.University of ParmaParmaItaly
  3. 3.Universitá di Milano BicoccaMilanItaly
  4. 4.Università di TrentoTrentoItaly
  5. 5.TriesteItaly

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