Abstract
Bosio generalized the construction by López de Medrano-Verjovsky- Meersseman (LVM) of a family of non-algebraic compact complex manifolds of any dimension. We describe how to construct the generalized family from certain Geometric Invariant Theory (GIT) quotients. We show that Bosio’s generalization parallels exactly the extension from Mumford’s GIT to the more general GIT developed by Białynicki-Birula and Świȩcicka. This point of view yields new results on the geometry of LVM and Bosio’s manifolds.
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Cupit-Foutou, S., Zaffran, D. Non-Kähler manifolds and GIT-quotients. Math. Z. 257, 783–797 (2007). https://doi.org/10.1007/s00209-007-0144-1
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DOI: https://doi.org/10.1007/s00209-007-0144-1