Real line arrangements with the Hirzebruch property

Panov, Dmitri

doi:10.2140/gt.2018.22.2697

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Real line arrangements with the Hirzebruch property

Dmitri Panov

Geometry & Topology 22 (2018) 2697–2711

DOI: 10.2140/gt.2018.22.2697

Abstract

A line arrangement of $3 n$ lines in $ℂ P^{2}$ 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 $ℂ P^{2}$ 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

Volume 22, issue 5 (2018)