Simple Geometric Characterization of Supersolvable Arrangements

Jiang, Tan; Yau, Shing‐Tung; Yeh, Larn-Ying

doi:10.1216/rmjm/1008959682

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Arrangements Of 10 Lines: An Example1

Introduction1

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2013

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Cited by 2 publications

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“…to F S ± respectively. Notice that F S ± are both fiber-type line arrangements according to Theorem 3.12 [JYY01] .…”

Section: Arrangements Of 10 Lines: An Examplementioning

confidence: 99%

Classification of moduli spaces of arrangements of nine projective lines

Ye¹

2013

Pacific J. Math.

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In the study of line arrangements, searching for minimal examples of line arrangements whose fundamental groups are not combinatorially invariant is a very interesting and hard problem. It was known that such a minimal arrangement must have at least 9 lines. In this paper, we extend the number to 10 by a new method. We classify arrangements of 9 projective lines according to the irreducibility of their moduli spaces and show that fundamental groups of complements of arrangements of 9 projective lines are combinatorially invariant. The idea and results have been used to classify arrangements of 10 projective lines.2000 Mathematics Subject Classification. 14N20, 32S22, 52C35.

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“…to F S ± respectively. Notice that F S ± are both fiber-type line arrangements according to Theorem 3.12 [JYY01] .…”

Section: Arrangements Of 10 Lines: An Examplementioning

confidence: 99%

Classification of moduli spaces of arrangements of nine projective lines

Ye¹

2013

Pacific J. Math.

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“…It is well known that fiber-type projective line arrangements are the same as supersolvable projective line arrangements (see, for example, [Orlik and Terao 1992]). Moreover, Jiang et al [2001] studied the geometric characterization of supersolvable line arrangements in ‫ސރ‬ 2 . They showed that any fiber-type line arrangement in ‫ސރ‬ 2 has a center through which every multiple point of the arrangement has a line in the arrangement passing.…”

Section: Introductionmentioning

confidence: 99%

A note on the topology of the complements of fiber-type line arrangements in ℂℙ²

Tan¹,

Yau²,

Ye³

2011

Pacific J. Math.

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Simple Geometric Characterization of Supersolvable Arrangements

Cited by 2 publications

References 6 publications

Classification of moduli spaces of arrangements of nine projective lines

Classification of moduli spaces of arrangements of nine projective lines

A note on the topology of the complements of fiber-type line arrangements in ℂℙ²

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Simple Geometric Characterization of Supersolvable Arrangements

Cited by 2 publications

References 6 publications

Classification of moduli spaces of arrangements of nine projective lines

Classification of moduli spaces of arrangements of nine projective lines

A note on the topology of the complements of fiber-type line arrangements in ℂℙ2

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A note on the topology of the complements of fiber-type line arrangements in ℂℙ²