The asymptotics of the holomorphic torsion forms

Martin Puchol

doi:10.1016/j.crma.2015.11.004

Analytic geometry/Differential geometry

The asymptotics of the holomorphic torsion forms
[L'asymptotique des formes de torsion holomorphe]

Présenté par : Jean-Michel Bismut

Martin Puchol ¹

¹ Université Paris Diderot - Paris 7, campus des Grands Moulins, bâtiment Sophie-Germain, case 7012, 75205 Paris cedex 13, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 301-306.

Résumé
Abstract

Dans cette note, nous utilisons la théorie des opérateurs de Toeplitz pour donner une formule asymptotique des formes de torsion analytique holomorphe associées à une famille de fibrés vectoriels holomorphes donnés par l'image directe de $L^{\otimes p}$ , où L est un fibré en droites. Pour obtenir cette asymptotique, nous faisons une hypothèse de positivité le long des fibres sur L. Ce résultat est la version en famille des résultats de Bismut et Vasserot sur la torsion holomorphe.

In this note, we use the theory of Toeplitz operators to give an asymptotic formula for the holomorphic analytic torsion forms associated with a family of holomorphic vector bundles that are the direct image of $L^{\otimes p}$ , where L is a line bundle. To obtain the asymptotics, we make a positivity assumption along the fibers on L. This result is the family version of the results of Bismut and Vasserot on the holomorphic torsion.

Reçu le : 2015-05-21
Accepté le : 2015-11-19
Publié le : 2016-01-27

DOI : 10.1016/j.crma.2015.11.004

Affiliations des auteurs :

Martin Puchol ¹

¹ Université Paris Diderot - Paris 7, campus des Grands Moulins, bâtiment Sophie-Germain, case 7012, 75205 Paris cedex 13, France

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Martin Puchol. The asymptotics of the holomorphic torsion forms. Comptes Rendus. Mathématique, Volume 354 (2016) no. 3, pp. 301-306. doi : 10.1016/j.crma.2015.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.11.004/

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