Quartic unexpected curves and surfaces

DOI10.1007/s00229-018-1091-3zbMath1432.14031arXiv1804.03610OpenAlexW2963810727WikidataQ128883605 ScholiaQ128883605MaRDI QIDQ2297352

Thomas Bauer, Tomasz Szemberg, Grzegorz Malara, Justyna Szpond

Publication date: 18 February 2020

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03610

zbMATH Keywords

point configurationslinear seriesunexpected varietiesexpected dimension

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15) Configurations and arrangements of linear subspaces (14N20)

Related Items (12)

Unexpected hypersurfaces with multiple fat points ⋮ Companion varieties for root systems and Fermat arrangements ⋮ Companion varieties for Hesse, Hesse union dual Hesse arrangements ⋮ Unexpected curves in \(\mathbb{P}^2\), line arrangements, and minimal degree of Jacobian relations ⋮ Diminished Fermat-type arrangements and unexpected curves ⋮ New constructions of unexpected hypersurfaces in \(\mathbb{P}^n\) ⋮ Unexpected hypersurfaces and where to find them ⋮ A matrixwise approach to unexpected hypersurfaces ⋮ On the unique unexpected quartic in \(\mathbb{P}^2\) ⋮ Unexpected surfaces singular on lines in \(\mathbb{P}^3\) ⋮ Sets of points which project to complete intersections, and unexpected cones ⋮ Hyperplane sections of the projective bundle associated to the tangent bundle of \(\mathbb{P}^2\)

Uses Software

• SINGULAR

Cites Work

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• Unexpected hypersurfaces with multiple fat points
• An asymptotic vanishing theorem for generic unions of multiple points
• Inverse system of a symbolic power. I
• On the unique unexpected quartic in \(\mathbb{P}^2\)
• Curve arrangements, pencils, and Jacobian syzygies
• Line arrangements and configurations of points with an unexpected geometric property
• On a class of special linear systems of $\mathbb{P}^3$
• Asymptotics of linear systems, with connections to line arrangements
• Singular hypersurfaces characterizing the Lefschetz properties

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