Berkovich skeleta and birational geometry

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Title: Berkovich skeleta and birational geometry
Authors: Nicaise, J
Item Type: Conference Paper
Abstract: We give a survey of joint work with Mircea Mustac{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.
Issue Date: 31-Dec-2016
Date of Acceptance: 1-Jan-2013
URI: http://hdl.handle.net/10044/1/30656
Publisher: Simons Symposium
Copyright Statement: © The Author
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 306610
Conference Name: Simons Symposium on Non-Archimedean Geometry and Tropical Geometry (March 31-April 6, 2013)
Keywords: math.AG
Notes: 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
Publication Status: Published
Start Date: 2013-03-31
Finish Date: 2013-04-06
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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