The second main theorem for holomorphic curves into semi-Abelian varieties

We apply these results to bound heights of cycles on moduli spaces of abelian varieties, induced by quotients of abelian varieties by levels of Barsotti-Tate subgroups, over

on the dassificatioa of the Abelian varieties p) re- presenting involutions which are generable by finite groups of automorphisms.. Next we remark that wp and all

We prove, using results of SMYTH [S], that if C is an irreducible curve of degree < 2n ifn <^ 7, and <^ 1.7719 n ifn > 7, on a simple principally polarized abelian variety

Otherwise, the image is of higher degree, in which case the line defined.. by general a points of C intersects this image

asks whether or not the field of moduli for a curve or a principally polarized abelian variety coincides with the residue field at the point on.. the coarse moduli

We continue to work in the "rational case" as in the preceding section; now also polarizations will be assumed to be defined over the ground field. The following result

The idea of the modification is roughly as follows: We use Ahlfors's theory in two steps (in several steps in general).. Hence, we can say t h a t our idea is the

CARLSOn, J., & GRI~FI~HS, P., A defect relation for equidimensional holomorphie mappings between algebraic varieties.. GRIFFITItS, P., I-Iolomorphie mappings: Survey