TITLE: what is large compex structure limit of CY moduli space
QUESTION [7 upvotes]: What is the Large Complex Structure limit(LCL) of complex moduli space of a Calabi-Yau 3-fold and why do we need to consider LCL in Mirror symmetry.

REPLY [4 votes]: The "large complex structure limit" is a family of CY manifolds
over a punctured disk having the maximal possible unipotent
(or, sometimes, quasiunipotent) monodromy. It seems that its existence is 
proven in this paper http://arxiv.org/abs/math/0008061
"Maximal Unipotent Monodromy for Complete Intersection CY Manifolds
Authors: Bong H. Lian, Andrey Todorov, Shing-Tung Yau"
for complete intersections. There are many claims of existence
of such family in other papers of Todorov, I am not sure how
much of them are correct. For simple examples (such as a K3)
it's not hard to find. 
You can also complete this family adding a fiber in the center
and call this fiber "a large complex structure limit", but this is
(apparently) not as useful.