Geometric height inequality on varieties with ample cotangent bundles

dc.creatorMoriwaki, Atsushi
dc.date1993-11-10
dc.date1993-12-08
dc.date.accessioned2026-07-07T08:57:48Z
dc.date.available2026-07-07T08:57:48Z
dc.descriptionLet F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F, and L a line bundle on X. In this note, we will prove that if the contangent bundle of X is ample and X is non-isotrivial, then there are a proper closed algebraic set Y of X and a constant A > 0 such that h_L(P) <= A d(P) + O(1) for all P \in X(\bar{F}) \ Y(\bar{F}), where h_L(P) is a geometric height of P with respect to L and d(P) is the geometric logarithmic discriminant of P. As corollary of the above height inequality, we can recover Noguchi's theorem, i.e. there is a non-empty Zariski open set U of X with U(F) = \emptyset.
dc.description9 pages, AmSTeX
dc.identifierhttps://arxiv.org/abs/alg-geom/9311003
dc.identifierhttp://arxiv.org/abs/alg-geom/9311003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147074
dc.subjectAlgebraic Geometry
dc.titleGeometric height inequality on varieties with ample cotangent bundles
dc.typetext

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