Johannes Nicaise
Published 2014-09-18Version 1
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.
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
Birational geometry of symplectic resolutions of nilpotent orbits II
Projective and birational geometry of Grassmannians and other special varieties
Birational geometry of terminal quartic 3-folds II: the importance of beings Q-factorial
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