Correlation for Surfaces of General Type

Details Correlation for Surfaces of General Type Correlation for Surfaces of General Type

1995-07-26

arxiv.org/abs/alg-geom/9507015v2

Mathematics

Algebraic Geometry

AMSLaTeX. This version contains some minor corrections, and additions to the references

Scientific paper

The main geometric result of this paper is that given any family of surfaces of general type f:X-->B, for sufficiently large n the fiber product X^n_B dominates a variety of general type. This result is especially interesting when it is combined with Lang's Conjecture. This states that for a variety V of general type over a number field K, the K rational points V(K) are not Zariski dense in V. Assuming Lang's Conjecture, we prove the existence of a uniform bound on the degree of the Zariski closure of the K-rational points of a surface of general type.

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