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Ramification conjecture and Hirzebruch’s property of line arrangements

Research output: Contribution to journalArticle

D. Panov, A. Petrunin

Original languageEnglish
Pages (from-to)2443-2460
Number of pages18
JournalCOMPOSITIO MATHEMATICA
Early online date25 Oct 2016
DOIs
Accepted/In press4 Jul 2016
E-pub ahead of print25 Oct 2016
PublishedDec 2016

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Abstract

The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral metrics on (Formula presented.) with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a (Formula presented.) ramification and prove this in several cases. In the latter case we prove that the ramification is (Formula presented.) if the metric on (Formula presented.) is non-negatively curved. We deduce that complex line arrangements in (Formula presented.) studied by Hirzebruch have aspherical complement.

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