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Seminários do IMPA

Geometria Diferencial

Título |
Deformation Limits of Various Classes of Compact Complex Manifolds |

Expositor |
Dan Popovici
Institut de Mathématiques de Toulouse |

Data |
Terça-feira, 4 de junho de 2019, 15:30 |

Local |
Sala 236. |

Resumo |

We prove that if in a holomorphic family of compact complex manifolds all the fibres, except possibly one, are Moishezon manifolds (i.e. bimeromorphically equivalent to projective manifolds), then the remaining, limiting, fibre is also Moishezon. Two new ingredients are introduced for this purpose: the Frolicher approximating vector bundle (FAVB) which displays the degenerating page of the Frolicher spectral sequence as the adiabatic limit, as a non-zero complex constant $h$ converges to $0$, of what we call the $d_h$-cohomology (where $d_h=h\partial + \bar\partial$); and new classes of Hermitian metrics that we call $E_r$-sG. A key step is to prove that any deformation limit of $\partial\bar\partial$-manifolds carries an $E_\infty$-sG metric.