Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces

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作者
Yusuke Kimura
机构
[1] KEK Theory Center,
[2] Institute of Particle and Nuclear Studies,undefined
[3] KEK,undefined
关键词
Differential and Algebraic Geometry; F-Theory; Gauge Symmetry; Superstring Vacua;
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摘要
F-theory/heterotic duality is formulated in the stable degeneration limit of a K3 fibration on the F-theory side. In this note, we analyze the structure of the stable degeneration limit. We discuss whether stable degeneration exists for pairs of rational elliptic surfaces. We demonstrate that, when two rational elliptic surfaces have an identical complex structure, stable degeneration always exists. We provide an equation that systematically describes the stable degeneration of a K3 surface into a pair of isomorphic rational elliptic surfaces. When two rational elliptic surfaces have different complex structures, whether their sum glued along a smooth fiber admits deformation to a K3 surface can be determined by studying the structure of the K3 lattice. We investigate the lattice theoretic condition to determine whether a deformation to a K3 surface exists for pairs of extremal rational elliptic surfaces. In addition, we discuss the configurations of singular fibers under stable degeneration.
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