The 21 Reducible Polars of Klein’s Quartic

DOI10.1080/10586458.2018.1488155zbMath1460.14071arXiv1803.06411OpenAlexW2794429437MaRDI QIDQ5857758

Joaquim Roé, Piotr Pokora

Publication date: 7 April 2021

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.06411

zbMATH Keywords

freenessline arrangementsplane curve arrangementsKlein quartic curvesymbolic and ordinary powers of ideals

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Plane and space curves (14H50) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Rational and birational maps (14E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisors, linear systems, invertible sheaves (14C20) Projective techniques in algebraic geometry (14N05)

Related Items (5)

Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems ⋮ Conic-line arrangements in the complex projective plane ⋮ Conic configurations via dual of quartic curves ⋮ Towards the weighted bounded negativity conjecture for blow-ups of algebraic surfaces ⋮ Harbourne constants, pull-back clusters and ramified morphisms

Uses Software

• SINGULAR

Cites Work

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• Freeness of conic-line arrangements in \(\mathbb P^{2}\)
• Generalized exponents of a free arrangement of hyperplanes and Shepherd- Todd-Brieskorn formula
• The configuration of bitangents of the Klein curve
• Comparison of symbolic and ordinary powers of ideals.
• On the containment problem
• Free and nearly free curves vs. rational cuspidal plane curves
• The orbifold Langer-Miyaoka-Yau inequality and Hirzebruch-type inequalities
• Polar covariants of plane cubics and quartics
• Ideal containments under flat extensions
• Counterexamples to the \(I^{(3)}\subset I^2\) containment
• Analytic projective geometry
• Harbourne constants and conic configurations on the projective plane
• Are symbolic powers highly evolved?
• Classical Algebraic Geometry
• Hirzebruch-type inequalities and plane curve configurations
• Bounded Negativity and Arrangements of Lines
• Splitting types of bundles of logarithmic vector fields along plane curves
• Asymptotics of linear systems, with connections to line arrangements
• Freeness versus maximal global Tjurina number for plane curves
• Uniform bounds and symbolic powers on smooth varieties

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