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Heights of Toric Varieties

Hertel, Julius Maximilian (2016) Heights of Toric Varieties. PhD, Universität Regensburg.

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Date of publication of this fulltext: 17 Feb 2016 14:09

Abstract (English)

We show that the toric local height of a toric variety with respect to a toric semipositive metrized line bundle over an arbitrary non-Archimedean field can be written as the integral over a polytope of a concave function. For discrete non-Archimedean fields, this was proved by Burgos-Philippon–Sombra (BPS). To show this statement, we first prove an induction formula for the non-Archimedean local ...

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Translation of the abstract (German)

Wir zeigen, dass die torische lokale Höhe einer torischen Varietät bezüglich eines torisch semipositiv metrisierten Geradenbündels über einem beliebigen nicht-archimedischen Körper als ein Integral einer konkaven Funktion über einem Polytop ausgedrückt werden kann. Für diskrete nicht-archimedische Körper wurde dies von Burgos-Philippon-Sombra (BPS) bewiesen. Um dieses Resultat zu zeigen, wird ...

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Item type:Thesis of the University of Regensburg (PhD)
Date:17 February 2016
Referee:Prof. Dr. Walter Gubler
Date of exam:28 January 2016
Institutions:Mathematics > Prof. Dr. Walter Gubler
Classification:
NotationType
14M25MSC
14G40MSC
14G22MSC
Keywords:toric variety, heights, Arakelov theory, metrized line bundle, Berkovich space, formal model
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:33291
Owner only: item control page

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