Faltings modular height and self-intersection of dualizing sheaf
| dc.creator | Moriwaki, Atsushi | |
| dc.date | 1994-02-17 | |
| dc.date.accessioned | 2026-07-07T09:06:00Z | |
| dc.date.available | 2026-07-07T09:06:00Z | |
| dc.description | Let 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.description | 10 pages, AmSTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9402013 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9402013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149869 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Faltings modular height and self-intersection of dualizing sheaf | |
| dc.type | text |