Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes · arXivDesk
1001.5312Jan 29, 2010The results of this paper are contained in "Period differential equations for the families of K3 surfaces with 2 parameters derived from the reflexive polytopes "
Period differential equations for families of K3 surfaces derived from some 3 dimensional reflexive polytopes
We study period maps for families of K3 surfaces those are given by anti canonical divisors of toric varieties coming from reflexive polytopes P2,P4,P5
Nearby in the stack
and
Pr
. We obtain systems of period differential equations for these families. Moreover, in the case
P4
, we determine the projective monodromy group of the period map. This group is explicitly related with the Hilbert modular group for