On K3 Surfaces with Large Complex Structure

2005/08/15 by Adrian Clingher, Clingher, Adrian, Charles F. Doran +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Geometry and complex manifolds #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.math/0508249

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

arxiv created 2005/08/24 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• Mirror Symmetry, Borcherd-Harvey-Moore Products and Determinants of the Calabi-Yau Metrics on K3 Surfaces

Related

• K3 Surfaces and String Duality
• Large Complex Structure Limits of K3 Surfaces
• Moduli of elliptic K3 surfaces: monodromy and Shimada root lattice strata
• Connected components of the moduli of elliptic K3 surfaces
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24