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2016 Combinatorial degenerations of surfaces and Calabi–Yau threefolds
Bruno Chiarellotto, Christopher Lazda
Algebra Number Theory 10(10): 2235-2266 (2016). DOI: 10.2140/ant.2016.10.2235


In this article we study combinatorial degenerations of minimal surfaces of Kodaira dimension 0 over local fields, and in particular show that the “type” of the degeneration can be read off from the monodromy operator acting on a suitable cohomology group. This can be viewed as an arithmetic analogue of results of Persson and Kulikov on degenerations of complex surfaces, and extends various particular cases studied by Matsumoto, Liedtke and Matsumoto, and Hernández Mada. We also study “maximally unipotent” degenerations of Calabi–Yau threefolds, following Kollár and Xu, showing in this case that the dual intersection graph is a 3-sphere.


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Bruno Chiarellotto. Christopher Lazda. "Combinatorial degenerations of surfaces and Calabi–Yau threefolds." Algebra Number Theory 10 (10) 2235 - 2266, 2016.


Received: 26 April 2016; Revised: 28 July 2016; Accepted: 5 September 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1354.14057
MathSciNet: MR3582018
Digital Object Identifier: 10.2140/ant.2016.10.2235

Primary: 14J28
Secondary: 11G25 , 14G20

Keywords: good reduction , Monodromy , surfaces

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.10 • No. 10 • 2016
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