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math.AG2005★ 1 cited
On K3 Surfaces with Large Complex Structure
Adrian Clingher, Charles F. Doran
We discuss a notion of large complex structure for elliptic K3 surfaces with section inspired by the eight-dimensional F-theory/heterotic duality in string theory. This concept is…
math.AG2005★ 79 cited
Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
Charles F. Doran, John W. Morgan
This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the in…
math.AG1998
Picard-Fuchs Uniformization: Modularity of the Mirror Map and Mirror-Moonshine
Charles F. Doran
Motivated by a conjecture of Lian and Yau concerning the mirror map in string theory, we determine when the mirror map q-series of certain elliptic curve and K3 surface families ar…