Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables

V. Maillot

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arXiv · alg-geom/9706005

Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables

V. Maillot

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Abstract

En nous appuyant sur une construction due à Bedford et Taylor, et certains résultats récents de Demailly, nous présentons une extension (partielle) de la géométrie d'Arakelov aux fibrés en droites intégrables. (Ces derniers sont les fibrés en droites hermitiens sur une variété arithmétique $X$ pouvant se décomposer sous la forme $\ov{E} = \ov{E}_{1}\otimes (\ov{E}_{2})^{-1}$, où $\ov{E}_{1}$ et $\ov{E}_{2}$ sont des fibrés en droites munis à l'infini d'une métrique continue approchable uniformément sur $X(C)$ par des métriques positives $C^{\infty}$). Nous appliquons notre théorie aux fibrés en droites sur une variété torique munis à l'infini de leur métrique canonique. Nous en déduisons, entre autres choses, la démonstration d'un analogue arithmétique du théorème de Bernstein-Koushnirenko.

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BibTeX RIS

V. Maillot. 1997-06-17. Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables. https://arxiv.org/abs/alg-geom/9706005

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