On the geography of line arrangements-Reference-Cited by-同舟云学术

On the geography of line arrangements

Published:2021-06-24 Issue:0 Volume:0 Page:
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Eterović Sebastian¹,Figueroa Fernando²,Urzúa Giancarlo³

Affiliation:

1. Department of Mathematics, University of California , Berkeley , USA

2. Department of Mathematics, Princeton University , Princeton USA

3. Facultad de Matemáticas, Pontificia Universidad Católica de Chile , Santiago , Chile

Abstract

Abstract We present various results about the combinatorial properties of line arrangements in terms of the Chern numbers of the corresponding log surfaces. This resembles the study of the geography of surfaces of general type. We prove some new results about the distribution of Chern slopes, we show a connection between their accumulation points and the accumulation points of linear H-constants on the plane, and we conclude with two open problems in relation to geography over ℚ and over ℂ.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0025/pdf

Reference17 articles.

1. T. Bauer, S. Di Rocco, B. Harbourne, J. Huizenga, A. Lundman, P. Pokora, T. Szemberg, Bounded negativity and arrangements of lines. Int. Math. Res. Not. no. 19 (2015), 9456–9471. MR3431599 Zbl 1330.14007

2. M. Cuntz, Minimal fields of definition for simplicial arrangements in the real projective plane. Innov. Incidence Geom. 12 (2011), 49–60. MR2942717 Zbl 1305.52026

3. N. G. de Bruijn, P. Erdös, On a combinatorial problem. Nederl. Akad. Wetensch., Proc. 51 (1948), 1277–1279 = Indagationes Math. 10 (1948), 421–423. MR28289 Zbl 0032.24405

4. S. Eterović, Logarithmic Chern slopes of arrangements of rational sections in Hirzebruch surfaces. Master Thesis, Pontificia Universidad Católica de Chile, Santiago 2015.

5. B. Grünbaum, A catalogue of simplicial arrangements in the real projective plane. Ars Math. Contemp. 2 (2009), 1–25. MR2485643 Zbl 1177.51020

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