Automorphism group of Batyrev Calabi-Yau threefolds
  In this paper, we will prove that all Batyrev Calabi-Yau threefolds, arising from a small resolution of a generic hyperplane section of a reflexive Fano-Gorenstein fourfold, have finite automorphism group. Together with Morrison conjecture, this suggests that Batyrev Calabi-Yau threefolds should have a polyhedral Kahler (ample) cone. 
Mohammad Farajzadeh Tehrani
math.AG math.SG