Degenerating Hodge structure of one-parameter family of Calabi-Yau   threefolds
  To a one-parameter family of Calabi-Yau threefolds, we can associate the extended period map by the log Hodge theory of Kato and Usui. In the present paper, we study the image of a maximally unipotent monodromy point under the extended period map. As an application, we prove the generic Torelli theorem for a large class of one-parameter families of Calabi-Yau threefolds. 
Tatsuki Hayama, Atsushi Kanazawa
math.AG math.CV