Semi-Stable Degeneration of Toric Varieties and Their Hypersurfaces

TL;DR

This paper constructs semistable degenerations of toric varieties using toric geometry, generalizing classical degenerations of K3 surfaces and providing new higher-dimensional examples and decompositions.

Contribution

It introduces a novel construction method for semistable degenerations of toric varieties and extends classical degenerations to higher dimensions.

Findings

Generalized degeneration of K3 surfaces into rational components

Decomposition of K3 as fiber sum of two E(1)'s

New examples of higher-dimensional degenerations

Abstract

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 it's higher dimensional generalizations, and many other new examples.