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Matthieu Madera

Publications and source records attributed to Matthieu Madera.

2 recordsLinked to original sources
arXiv2025

Deformations of geometric structures on a subclass of LVM threefolds

We study deformations of geometric structures on some LVM manifolds of complex dimension $3$. More precisely, we study resonant structures, a particular type of $(G,X)$-structures, via the Ehresmann-Thurston principle, and their link with the deformation of the complex structure of the LVM manifold in the sense of Kodaira, Spencer and Kuranishi. We describe the Kuranishi family of these manifolds and construct a family containing all of them and complete at every point.

math.DG↗
arXiv2025

Holomorphic geometric structures on Hopf manifolds

We construct integrable holomorphic G-structures and flat holomorphic Cartan geometries on every complex Hopf manifold, without using the normal forms given by the Poincar\'e-Dulac Theorem. We provide a new proof of the latter using charts adapted with the geometric structures.

math.DG↗