A note on the automorphism group of a compact complex manifold
Laurent Meersseman (LAREMA)

TL;DR
This paper provides explicit examples of compact complex 3-folds with automorphisms isotopic to the identity via smooth diffeomorphisms but not through biholomorphisms, impacting the study of Teichmüller stacks.
Contribution
It introduces specific examples illustrating a nuanced difference in automorphism isotopies relevant to higher-dimensional Teichmüller theory.
Findings
Existence of automorphisms isotopic to identity via smooth but not holomorphic deformations
Examples relevant for the construction of higher-dimensional Teichmüller stacks
Highlights subtle distinctions in automorphism groups of complex manifolds
Abstract
In this note, we give explicit examples of compact complex 3-folds which admit automorphisms that are isotopic to the identity through C -diffeomorphisms but not through biholomorphisms. These automorphisms play an important role in the construction of the Te-ichm{\"u}ller stack of higher dimensional manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry
