When does the Hessian determinant vanish identically? (On Gordan and Noether's proof of Hesse's claim)

DOI10.1007/s00574-004-0004-0zbMath1061.12002OpenAlexW2325889330MaRDI QIDQ1882733

Christoph Lossen

Publication date: 1 October 2004

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-004-0004-0

zbMATH Keywords

polynomialhomogeneous polynomialHessian determinant

Mathematics Subject Classification ID

Jacobian problem (14R15) Hypersurfaces and algebraic geometry (14J70) Real and complex fields (12D99)

Related Items (19)

Homogeneous quasi-translations in dimension 5 ⋮ The Generalized Baker–Schmidt Problem on Hypersurfaces ⋮ Quasi-translations and singular Hessians ⋮ On higher Hessians and the Lefschetz properties ⋮ A theorem of Gordan and Noether via Gorenstein rings ⋮ Logarithmic Hesse's problem ⋮ Perazzo hypersurfaces and the weak Lefschetz property ⋮ On Polynomials with Vanishing Hessians and Some Density Problems ⋮ Waring problems and the Lefschetz properties ⋮ Lefschetz properties of some codimension three Artinian Gorenstein algebras ⋮ Perazzo 3-folds and the weak Lefschetz property ⋮ On cubic hypersurfaces with vanishing Hessian ⋮ Global properties of toric nearly Kähler manifolds ⋮ Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian ⋮ On mixed Hessians and the Lefschetz properties ⋮ On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version) ⋮ On the gradient conjecture for quadratic polynomials ⋮ A geometrical approach to Gordan-Noether's and Franchetta's contributions to a question posed by Hesse ⋮ Hypersurfaces with vanishing Hessian via Dual Cayley Trick

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