A Remark on Projective Embeddings of Varieties with Non-Negative   Cotangent Bundles
  We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow (almost) exponentially in the dimension of X. 
Lawrence Ein, Bo Ilic and Robert Lazarsfeld