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arXiv · 2009.13596

An Analytic Proof of the Stable Reduction Theorem

Jian Song·Jacob Sturm·Xiaowei Wang
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Abstract

The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this result for curves defined over $\mathbb{C}$ using the K\"ahler-Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.

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Jian Song, Jacob Sturm, Xiaowei Wang. 2020-09-28. An Analytic Proof of the Stable Reduction Theorem. https://arxiv.org/abs/2009.13596

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