Volume 22, issue 5 (2018)

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Real line arrangements with the Hirzebruch property

Dmitri Panov

Geometry & Topology 22 (2018) 2697–2711

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.

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