Faltings modular height and self-intersection of dualizing sheaf

dc.creatorMoriwaki, Atsushi
dc.date1994-02-17
dc.date.accessioned2026-07-07T09:06:00Z
dc.date.available2026-07-07T09:06:00Z
dc.descriptionLet K be a number field, O_K the ring of integers of K and X a stable curve over O_K of genus g >= 2. In this note, we will prove a strict inequality ( (K_{X/S})^2 / [K : Q] ) > Height_{Fal}(J(X_K)), where $K_{X/S}$ is the canonically metrized dualizing sheaf of X over S = Spec(O_K) and Height_{Fal}(J(X_K)) is the Faltings modular height of the Jacobian of X_K. As corollary, for any constant A, the set of all stable curves X over O_K with ( (K_{X/S})^2 / [K : Q] ) <= A is finite under the following equivalence. For stable curves X and Y, X is equivalent to Y if X is isomorphic to Y over O_{K'} for some finite extension field K' of K.
dc.description10 pages, AmSTeX
dc.identifierhttps://arxiv.org/abs/alg-geom/9402013
dc.identifierhttp://arxiv.org/abs/alg-geom/9402013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149869
dc.subjectAlgebraic Geometry
dc.titleFaltings modular height and self-intersection of dualizing sheaf
dc.typetext

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