Semistable Degeneration of Toric Varieties and Their Hypersurfaces

We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of $K3$ surface into 4 rational components, an algebraic geometric version of decomposing $K3$ as the fiber sum of two $E(1)$'s as well as its higher dimensional generalizations and many other new examples.

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Published 1 January 2006