Adrian Clingher, Charles F. Doran
Published 2005-08-15, updated 2005-08-24Version 2
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 naturally associated with the Type II Mumford partial compactification of the moduli space of periods for these structures. The paper provides an explicit Hodge-theoretic condition for the complex structure of an elliptic K3 surface with section to be large. We also discuss certain geometrical implications of this large complex structure condition in terms of the Kodaira types of the singular fibers of the elliptic fibration.
Comments: 27 pages, latex, typos corrected, minor revision of section 2
An elliptic K3 surface associated to Heron triangles
Connected components of the moduli of elliptic K3 surfaces
Mordell-Weil groups and automorphism groups of elliptic K3 surfaces
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