Ramification conjecture and Hirzebruch's property of line arrangements

D. Panov, A. Petrunin

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 CP2 with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a CAT[0] ramification and prove this in several cases. In the latter case we prove that the ramification is CAT[0] if the metric on CP2 is non-negatively curved. We deduce that complex line arrangements in CP2 studied by Hirzebruch have aspherical complement.

Original languageEnglish (US)
Pages (from-to)2443-2460
Number of pages18
JournalCompositio Mathematica
Volume152
Issue number12
DOIs
StatePublished - Dec 1 2016

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Property of line
Ramification
CAT(0)
Arrangement
Metric
Universal Cover
Quotient Space
Line
Discrete Group
Isometry
Locus
Completion
Euclidean space
Deduce
Quotient
Complement
Singularity

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Ramification conjecture and Hirzebruch's property of line arrangements. / Panov, D.; Petrunin, A.

In: Compositio Mathematica, Vol. 152, No. 12, 01.12.2016, p. 2443-2460.

Research output: Contribution to journalArticle

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