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arXiv · 1207.1048

A tour of stable reduction with applications

Sebastian Casalaina-Martin
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Abstract

The Deligne-Mumford stable reduction theorem asserts that for a family of stable curves over the punctured disk, after a finite base change, the family can be completed in a unique way to a family of stable curves over the disk. In this survey we discuss stable reduction theorems in a number of different contexts. This includes a review of recent results on abelian varieties, canonically polarized varieties, and singularities. We also consider the semi-stable reduction theorem and results concerning simultaneous stable reduction.

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Sebastian Casalaina-Martin. 2012-07-04. A tour of stable reduction with applications. https://arxiv.org/abs/1207.1048

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