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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Real line arrangements with the Hirzebruch property

Dmitri Panov

Geometry & Topology 22 (2018) 2697–2711
Abstract

A line arrangement of 3n lines in P2 satisfies the Hirzebruch property if each line intersect others in n + 1 points. Hirzebruch asked in 1985 if all such arrangements are related to finite complex reflection groups. We give a positive answer to this question in the case when the line arrangement in P2 is real, confirming that there exist exactly four such arrangements.

Keywords
line arrangements, complex reflection groups, polyhedral manifolds, Kähler metrics
Mathematical Subject Classification 2010
Primary: 14N20, 32S22, 51F15, 52B70, 53C55
Secondary: 20F55, 32Q15
References
Publication
Received: 4 August 2016
Accepted: 29 January 2018
Published: 1 June 2018
Proposed: Dmitri Burago
Seconded: Bruce Kleiner, Dan Abramovich
Authors
Dmitri Panov
Department of Mathematics
King’s College London
London
United Kingdom