English

Some examples due to H. Hironaka

Algebraic Geometry 2015-03-30 v2 Complex Variables

Abstract

The aim of this paper is to explain the construction by H. Hironaka [H.61] of a holomorphic (in fact "algebraic") family of compact complex manifolds parametrized by \C\C such for all s\C{0}s \in \C\setminus \{0\} the fiber is projective, but such that the fiber at the origin in non k{\"a}hlerian, to mathematicians which are not algebraic geometers. We also explain why it is not possible to make in the same way such an example with fiber at 00 a simpler example of non k{\"a}hlerian Moishezon manifold which is also due to H. Hironaka (see section 5).

Keywords

Cite

@article{arxiv.1501.01129,
  title  = {Some examples due to H. Hironaka},
  author = {Daniel Barlet},
  journal= {arXiv preprint arXiv:1501.01129},
  year   = {2015}
}

Comments

Some more explanations and comments added

R2 v1 2026-06-22T07:52:11.595Z