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- W3101471827 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 $mathbb{C}text{P}^{2}$ with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a $text{CAT}[0]$ ramification and prove this in several cases. In the latter case we prove that the ramification is $text{CAT}[0]$ if the metric on $mathbb{C}text{P}^{2}$ is non-negatively curved. We deduce that complex line arrangements in $mathbb{C}text{P}^{2}$ studied by Hirzebruch have aspherical complement." @default.
- W3101471827 created "2020-11-23" @default.
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- W3101471827 date "2016-10-25" @default.
- W3101471827 modified "2023-10-14" @default.
- W3101471827 title "Ramification conjecture and Hirzebruch’s property of line arrangements" @default.
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- W3101471827 doi "https://doi.org/10.1112/s0010437x16007648" @default.
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