no. 1-2
Algebraic Geometry/Analytic Geometry
A natural hermitian metric associated with local universal families of compact Kähler manifolds with zero first Chern class
[Une forme hermitienne naturelle associée aux familles de variétés compactes Kähleriennes dont la première classe de Chern est nulle]

Présenté par : Jean-Pierre Demailly

Magnússon, Gunnar1
1 Institut Fourier, 100, rue des Maths, BP 74, 38402 St Martin dʼHères, France
Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 63-66.

Soit π:X→S une famille universelle locale de variétés compactes Kähleriennes dont la première classe de Chern est nulle sur une base lisse S. Les cônes de Kähler complexifiés de chaque variété de la famille forment une fibration holomorphe K→S. Nous montrons quʼil existe une métrique hermitienne naturelle sur le produit fibré X×SK. Pour finir, nous discutons lʼexemple des courbes elliptiques.

Let π:X→S be a local universal family of compact Kähler manifolds with zero first Chern class over a smooth base S. The complexified Kähler cones of each manifold of the family form a holomorphic fiber bundle K→S. We show that there exists a natural hermitian metric ω on the fiber product X×SK. We then discuss the example of elliptic curves in some detail.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.11.013
Magnússon, Gunnar 1

1 Institut Fourier, 100, rue des Maths, BP 74, 38402 St Martin dʼHères, France 
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Magnússon, Gunnar. A natural hermitian metric associated with local universal families of compact Kähler manifolds with zero first Chern class. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 63-66. doi : 10.1016/j.crma.2011.11.013. http://www.numdam.org/articles/10.1016/j.crma.2011.11.013/

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