On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version)

DOI10.1007/978-3-030-42136-6_3zbMath1455.14118arXiv1703.07624OpenAlexW3169682193MaRDI QIDQ4964376

Michiel de Bondt, Junzo Watanabe

Publication date: 25 February 2021

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.07624

zbMATH Keywords

homogeneous polynomialHessian form

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Actions of groups on commutative rings; invariant theory (13A50) Classification of affine varieties (14R05) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) Hypersurfaces and algebraic geometry (14J70)

Related Items (6)

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Cites Work

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• Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
• A geometrical approach to Gordan-Noether's and Franchetta's contributions to a question posed by Hesse
• Homogeneous quasi-translations in dimension 5
• Quadratic polynomial maps with Jacobian rank two
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• When does the Hessian determinant vanish identically? (On Gordan and Noether's proof of Hesse's claim)
• Singular Hessians
• Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials
• Quasi-translations and singular Hessians

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