# Geometric Lang conjecture - reference

In their paper "Uniformity of rational points", Caporaso, Harris, and Mazur asserted the following:

"The Geometric Lang conjecture has been proved for all surfaces with $c_1^2 > c_2$ ([B]), and has recently been announced for all surfaces ([LM])."

The referece [LM] in that paper (link here: http://www.ams.org/journals/jams/1997-10-01/S0894-0347-97-00195-1/S0894-0347-97-00195-1.pdf) is a preprint by S. Lu and M. Miyaoka, with no title. Their paper was published in 1997, so surely this preprint should be published by now, but I am unable to find it. Does anyone know the actual title of the paper, and perhaps what journal it is published in?

• The paper is Bounding curves in algebraic surfaces by genus and Chern numbers. Math. Res. Lett. 2 (1995), no. 6, 663-676 (the Caporaso-Harris-Mazur paper was accepted in revised form early 1995). However, Lu and Miyaoka prove only a weak form of the geometric Lang conjecture, namely that there are only finitely many smooth rational or elliptic curves on a surface of general type. – abx Jan 15 '18 at 16:18

For a comparison you may recall that in the arithmetic case, for arithmetic surfaces (algebraic curves), Vojta has proved a weaker form of his conjecture that has an arithmetic discriminant term $d_a(P)$ in place of a field discriminant term and which, in contrast to the Vojta conjecture, is far too weak to be adequate for deriving any consequence about the $abc$ conjecture.