English

Berkovich skeleta and birational geometry

Algebraic Geometry 2014-09-19 v1

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.

Cite

@article{arxiv.1409.5229,
  title  = {Berkovich skeleta and birational geometry},
  author = {Johannes Nicaise},
  journal= {arXiv preprint arXiv:1409.5229},
  year   = {2014}
}

Comments

These are expanded lecture notes of a talk at the Simons Symposium on Non-Archimedean Geometry and Tropical Geometry (March 31-April 6, 2013). They have been submitted to the conference proceedings

R2 v1 2026-06-22T05:59:30.803Z