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L. Meersseman - Kuranishi and TeichmüllerSummer School 2019 - Foliations and algebraic geometry


Description : 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.
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Submitted on : Friday, August 30, 2019 - 12:14:10 PM
Last modification on : Wednesday, November 3, 2021 - 9:18:41 AM