On complex supersolvable line arrangements

Takuro Abe; Alexandru Dimca

doi:10.1016/j.jalgebra.2020.02.007

On complex supersolvable line arrangements

Takuro Abe, Alexandru Dimca

Division of Fundamental mathematics

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

1 Citation (Scopus)

Abstract

We show that the number of lines in an m–homogeneous supersolvable line arrangement is upper bounded by 3m−3 and we classify the m–homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. We also prove the nonexistence of unexpected curves for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements having a generic vertex.

Original language	English
Pages (from-to)	38-51
Number of pages	14
Journal	Journal of Algebra
Volume	552
DOIs	https://doi.org/10.1016/j.jalgebra.2020.02.007
Publication status	Published - Jun 15 2020

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2020.02.007

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title = "On complex supersolvable line arrangements",

abstract = "We show that the number of lines in an m–homogeneous supersolvable line arrangement is upper bounded by 3m−3 and we classify the m–homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. We also prove the nonexistence of unexpected curves for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements having a generic vertex.",

author = "Takuro Abe and Alexandru Dimca",

note = "Funding Information: This work is partially supported by KAKENHI, JSPS Grant-in-Aid for Scientific Research (B) 16H03924.This work has been supported by the French government, through the UCAJEDI Investments in the Future project managed by the French National Research Agency (ANR) with the reference number ANR-15-IDEX-01 and by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030, within PNCDI III. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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doi = "10.1016/j.jalgebra.2020.02.007",

language = "English",

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AU - Abe, Takuro

AU - Dimca, Alexandru

N1 - Funding Information: This work is partially supported by KAKENHI, JSPS Grant-in-Aid for Scientific Research (B) 16H03924.This work has been supported by the French government, through the UCAJEDI Investments in the Future project managed by the French National Research Agency (ANR) with the reference number ANR-15-IDEX-01 and by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030, within PNCDI III. Publisher Copyright: © 2020 Elsevier Inc.

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N2 - We show that the number of lines in an m–homogeneous supersolvable line arrangement is upper bounded by 3m−3 and we classify the m–homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. We also prove the nonexistence of unexpected curves for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements having a generic vertex.

AB - We show that the number of lines in an m–homogeneous supersolvable line arrangement is upper bounded by 3m−3 and we classify the m–homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. We also prove the nonexistence of unexpected curves for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements having a generic vertex.

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VL - 552

SP - 38

EP - 51

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

On complex supersolvable line arrangements

Abstract

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