Skip to main content
MathOverflow

Return to Question

added 54 characters in body; edited tags
Source Link
user21574
user21574

A well-known example in the deformation theory of compact complex manifolds is the one given by Hironaka in his 1962 paper An Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian Complex StructuresAn Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian Complex Structures. The construction gives rise to many interesting phenomena (see the associated Wikipedia article), but the one that interests me most is that this was the first example of a deformation of Kähler manifolds which has limiting fibre which is not Kähler.

Aside from Hironaka's example, are there any other explicit deformations of compact Kähler manifolds such that the central fibre is not Kähler?

A well-known example in the deformation theory of compact complex manifolds is the one given by Hironaka in his 1962 paper An Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian Complex Structures. The construction gives rise to many interesting phenomena (see the associated Wikipedia article), but the one that interests me most is that this was the first example of a deformation of Kähler manifolds which has limiting fibre which is not Kähler.

Aside from Hironaka's example, are there any other explicit deformations of compact Kähler manifolds such that the central fibre is not Kähler?

A well-known example in the deformation theory of compact complex manifolds is the one given by Hironaka in his 1962 paper An Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian Complex Structures. The construction gives rise to many interesting phenomena (see the associated Wikipedia article), but the one that interests me most is that this was the first example of a deformation of Kähler manifolds which has limiting fibre which is not Kähler.

Aside from Hironaka's example, are there any other explicit deformations of compact Kähler manifolds such that the central fibre is not Kähler?

Source Link
Michael Albanese
Michael Albanese
  • 19.3k
  • 9
  • 87
  • 160

Is Hironaka's example the only known deformation of Kähler manifolds with non-Kähler central fibre?

A well-known example in the deformation theory of compact complex manifolds is the one given by Hironaka in his 1962 paper An Example of a Non-Kählerian Complex-Analytic Deformation of Kählerian Complex Structures. The construction gives rise to many interesting phenomena (see the associated Wikipedia article), but the one that interests me most is that this was the first example of a deformation of Kähler manifolds which has limiting fibre which is not Kähler.

Aside from Hironaka's example, are there any other explicit deformations of compact Kähler manifolds such that the central fibre is not Kähler?