Nonexistence of asymptotic GIT compactification

@article{Wang2014NonexistenceOA,
  title={Nonexistence of asymptotic GIT compactification},
  author={Xiaowei Wang and Xu Chen},
  journal={Duke Mathematical Journal},
  year={2014},
  volume={163},
  pages={2217-2241}
}
We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in $P^3$ with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize. 
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