On K3 Surfaces with Large Complex Structure

Details On K3 Surfaces with Large Complex Structure On K3 Surfaces with Large Complex Structure

2005-08-15

arxiv.org/abs/math/0508249v2

Mathematics

Algebraic Geometry

27 pages, latex, typos corrected, minor revision of section 2

Scientific paper

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.

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