A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2007; you can also visit the original URL.
The file type is application/pdf
.
Picard–Fuchs Uniformization and Modularity¶of the Mirror Map
2000
Communications in Mathematical Physics
Arithmetic properties of mirror symmetry (type IIA-IIB string duality) are studied. We give criteria for the mirror map q-series of certain families of Calabi-Yau manifolds to be automorphic functions. For families of elliptic curves and lattice polarized K3 surfaces with surjective period mappings, global Torelli theorems allow one to present these criteria in terms of the ramification behavior of natural algebraic invariants -the functional and generalized functional invariants respectively.
doi:10.1007/s002200000228
fatcat:aqfkgcgy5vggpcvddy2csy7ohe