Real line arrangements with Hirzebruch property

Dmitri Panov

doi:10.2140/gt.2018.22.2697

Real line arrangements with Hirzebruch property

Dmitri Panov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

A line arrangement of 3n lines in ℂP² 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 ℂP² is real, confirming that there exist exactly four such arrangements.

Original language	English
Pages (from-to)	2697-2711
Number of pages	15
Journal	Geometry & Topology
Volume	22
Issue number	5
Early online date	1 Jun 2018
DOIs	https://doi.org/10.2140/gt.2018.22.2697
Publication status	Published - Jun 2018

Keywords

Complex reflection groups
Kähler metrics
Line arrangements
Polyhedral manifolds

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10.2140/gt.2018.22.2697

Real line arrangements with_PANOV_Accepted 29 January 2018_GREEN AAMAccepted author manuscript, 281 KB

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abstract = "A line arrangement of 3n lines in ℂP2 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 ℂP2 is real, confirming that there exist exactly four such arrangements.",

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KW - Polyhedral manifolds

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Real line arrangements with Hirzebruch property

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