Some examples due to H. Hironaka - Institut Élie Cartan de Lorraine

Date/heure
19 janvier 2015
14:00 - 15:00

Oratrice ou orateur
Daniel Barlet

Catégorie d'évènement
Séminaire de géométrie complexe

Résumé

The aim of this paper is to give some comments on the construction by H. Hironaka [H.61] of a holomorphic (in fact algebraic) family of compact complex manifolds parametrized by $m a t h b b C$ such for all $u i n m a t h b b C s e t m i n u s 0$ the fiber is projective, but such that the fiber at the origin is non kählerian. We also explain why it is not possible to make in the same way such a family with fiber at $0$ a simpler example of non kählerian Moishezon manifold which is also due to H. Hironaka.

This paper does not give a complete proof of Hironaka’s construction. It only tries to give some help for the reader of this famous article and tries to explain some points which are not explicit although they are well known to specialists.