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arXiv · 1409.5229

Berkovich skeleta and birational geometry

Johannes Nicaise
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Abstract

We give a survey of joint work with Mircea Musta\c{t}\u{a} and Chenyang Xu on the connections between the geometry of Berkovich spaces over the field of Laurent series and the birational geometry of one-parameter degenerations of smooth projective varieties. The central objects in our theory are the weight function and the essential skeleton of the degeneration. We tried to keep the text self-contained, so that it can serve as an introduction to Berkovich geometry for birational geometers.

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Johannes Nicaise. 2014-09-18. Berkovich skeleta and birational geometry. https://arxiv.org/abs/1409.5229

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