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Videos Year : 2019

L. Meersseman - Kuranishi and Teichmüller


Fanny Bastien
Donovan Humphries
  • Function : Director


Let X be a compact complex manifold. The Kuranishi space of X is an analytic space which encodes every small deformation of X. The Teichmüller space is a topological space formed by the classes of compact complex manifolds diffeomorphic to X up to biholomorphisms smoothly isotopic to the identity. F. Catanese asked when these two spaces are locally homeomorphic. Unfortunatly, this almost never occurs. I will reformulate this question replacing these two spaces with stacks. I will then show that, if X is Kähler, this new question has always a positive answer. Finally, I will discuss the non-Kähler case.

Dates and versions

medihal-02274908 , version 1 (30-08-2019)


Attribution - NonCommercial - NoDerivatives


  • HAL Id : medihal-02274908 , version 1


Laurent Meersseman, Fanny Bastien, Donovan Humphries. L. Meersseman - Kuranishi and Teichmüller: Summer School 2019 - Foliations and algebraic geometry. 2019. ⟨medihal-02274908⟩
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