Continuity of volumes on arithmetic varieties

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dc.creatorMoriwaki, Atsushi
dc.date2006-12-11
dc.date2007-01-06
dc.date.accessioned2026-07-07T07:38:49Z
dc.date.available2026-07-07T07:38:49Z
dc.descriptionWe introduce the volume function for hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef hermitian invertible sheaf. We also give another several applications, for example, a generalized Hodge index theorem, an arithmetic Bogomolov-Gieseker's inequality, etc.
dc.descriptionadd applications
dc.identifierhttps://arxiv.org/abs/math/0612269
dc.identifierhttp://arxiv.org/abs/math/0612269
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121229
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject14G40, 11G50
dc.titleContinuity of volumes on arithmetic varieties
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