Geometric height inequality on varieties with ample cotangent bundles
| dc.creator | Moriwaki, Atsushi | |
| dc.date | 1993-11-10 | |
| dc.date | 1993-12-08 | |
| dc.date.accessioned | 2026-07-07T08:57:48Z | |
| dc.date.available | 2026-07-07T08:57:48Z | |
| dc.description | Let 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.description | 9 pages, AmSTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9311003 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9311003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147074 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Geometric height inequality on varieties with ample cotangent bundles | |
| dc.type | text |