A high fibered power of a family of varieties of general type dominates a variety of general type

Abstract

We prove the following theorem: Fibered Power Theorem: Let $X\rar B$ be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general type $W_n$, and a dominant rational map $X^n_B \das W_n$.