# Autour du programme de Calabi, méthodes de recollement

Abstract : We study the existence of metrics of constant Hermitian scalar curvature on almost-Kähler manifolds obtained as smoothings of a constant scalar curvature Kähler orbifold, with $A_1$ singularities. More precisely, given such an orbifold that does not admit nontrivial holomorphic vector fields, we show that an almost-Kähler smoothing $(M_\varepsilon, \omega_\varepsilon)$ admits an almost-Kähler structure $(J_\varepsilon, g_\varepsilon)$ of constant Hermitian curvature. Moreover, we show that for $\varepsilon > 0$ small enough, the $(M_\varepsilon, \omega_\varepsilon)$ are all symplectically equivalent to a fixed symplectic manifold $(M , \omega)$ in which there is a surface $S$ homologous to a 2-sphere, such that $[S]$ is a vanishing cycle that admits a representant that is Hamiltonian stationary for $g_\varepsilon$.
Keywords :
Document type :
Theses

Cited literature [13 references]

https://tel.archives-ouvertes.fr/tel-01912801
Contributor : Caroline Vernier <>
Submitted on : Monday, November 5, 2018 - 4:48:12 PM
Last modification on : Monday, March 25, 2019 - 4:52:06 PM
Long-term archiving on: Wednesday, February 6, 2019 - 3:50:14 PM

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• HAL Id : tel-01912801, version 1

### Citation

Caroline Vernier. Autour du programme de Calabi, méthodes de recollement. Géométrie différentielle [math.DG]. Université Bretagne Loire, 2018. Français. ⟨tel-01912801v1⟩

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