English

Zariski pairs on cubic surfaces

Algebraic Geometry 2025-09-16 v2
Authors: Ichiro Shimada
View on arXiv ↗ PDF ↗

Abstract

A line arrangement of a smooth cubic surface is a subset of the set of lines on the cubic surface. We define a notion of Zariski pairs of line arrangements on general cubic surfaces, and make the complete list of these Zariski pairs.

Keywords

cubic fourfolds

Cite

@article{arxiv.2401.15930,
  title  = {Zariski pairs on cubic surfaces},
  author = {Ichiro Shimada},
  journal= {arXiv preprint arXiv:2401.15930},
  year   = {2025}
}

Comments

7 pages. Some new references have been added

Related papers

View all related →
Algebraic Geometry · Mathematics
Rational points of elliptic surfaces and Zariski $N$-ples for cubic-line, cubic-conic-line arrangements
Shinzo Bannai, Hiro-o Tokunaga, Momoko Yamamoto
2017-11-15
Algebraic Geometry · Mathematics
On the Abel-Jacobi map of an elliptic surface and the topology of cubic-line arrangements
Shinzo Bannai, Hiro-o Tokunaga
2018-02-20
Algebraic Geometry · Mathematics
A note on the topology of arrangements for a smooth plane quartic and its bitangent lines
Shinzo Bannai, Hiro-o Tokunaga, Momoko Yamamoto
2018-06-11
Algebraic Geometry · Mathematics
Trisections on Certain Rational Elliptic Surfaces and Families of Zariski Pairs Degenerating to the same Conic-line Arrangement
S. Bannai, N. Kawana, R. Masuya, H. Tokunaga
2021-03-16
Algebraic Geometry · Mathematics
Zariski pairs of conic-line arrangements with a unique conic
Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane
2024-10-08
Algebraic Geometry · Mathematics
On the topology of arrangements of a cubic and its inflectional tangents
Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane, Hiro-o Tokunaga
2016-07-27
alg-geom · Mathematics
A note on Zariski pairs
Ichiro Shimada
2008-02-03
Algebraic Geometry · Mathematics
Detecting Zariski Pairs by Algorithms and Computational Classification in Conic Line Arrangements
Meirav Amram, Gal Goren
2026-01-05
Algebraic Geometry · Mathematics
96120: The degree of the linear orbit of a cubic surface
Laura Brustenga i Moncusí, Sascha Timme, Madeleine Weinstein
2019-10-22
Algebraic Geometry · Mathematics
Rational lines on smooth cubic surfaces
Stephen McKean
2025-03-04
Algebraic Geometry · Mathematics
Moduli spaces of ten-line arrangements with double and triple points
Meirav Amram, Moshe Cohen, Mina Teicher, Fei Ye
2013-06-27
Algebraic Geometry · Mathematics
A surface containing a line and a circle through each point is a quadric
Fedor Nilov, Mikhail Skopenkov
2014-01-28
Algebraic Geometry · Mathematics
Zariski $N$-ples for a smooth cubic and its tangent lines
Shinzo Bannai, Hiro-o Tokunaga
2019-03-12
Algebraic Geometry · Mathematics
Zariski decompositions on arithmetic surfaces
Atsushi Moriwaki
2011-01-26
Metric Geometry · Mathematics
Cubic Polyhedra
Chaim Goodman-Strauss, John M Sullivan
2007-05-23
Algebraic Geometry · Mathematics
Zariski pairs of conic-line arrangements of degrees 7 and 8 via fundamental groups
Meirav Amram, Robert Shwartz, Uriel Sinichkin, Sheng-Li Tan +1
2025-03-26
Algebraic Geometry · Mathematics
Apparent contours of nonsingular real cubic surfaces
Sergey Finashin, Viatcheslav Kharlamov
2015-02-10
Algebraic Geometry · Mathematics
The realization space of a certain conic line arrangement of degree 7 and a $\pi_1$-equivalent Zariski pair
Meirav Amram, Shinzo Bannai, Taketo Shirane, Uriel Sinichkin +1
2023-07-06
Algebraic Geometry · Mathematics
Counting lines on surfaces
Samuel Boissiere, Alessandra Sarti
2007-05-23
Algebraic Geometry · Mathematics
Examples of strong Ziegler pairs of conic-line arrangements of degree 7 and 8
Shinzo Bannai, Hiro-o Tokunaga
2025-09-11
Geometric Topology · Mathematics
An arithmetic Zariski 4-tuple of twelve lines
Benoît Guerville-Ballé
2016-03-09
Combinatorics · Mathematics
Combinatorial configurations, quasiline arrangements, and systems of curves on surfaces
Jürgen Bokowski, Jurij Kovič, Tomaž Pisanski, Arjana Žitnik
2014-10-10
Algebraic Geometry · Mathematics
Explicit computations of Zariski decompositions on P_Z^1
Atsushi Moriwaki
2010-02-11
Algebraic Geometry · Mathematics
Twenty-Seven Questions about the Cubic Surface
Kristian Ranestad, Bernd Sturmfels
2019-12-17
Algebraic Geometry · Mathematics
On the Abel-Jacobi map for bisections of rational elliptic surfaces and Zariski $N$-plet for conic arrangements
Shinzo Bannai, Hiro-O Tokunaga
2012-12-20
R2 v1 2026-06-28T14:29:48.704Z