On cubic hypersurfaces with vanishing Hessian

DOI10.1016/j.jpaa.2014.04.030zbMath1318.14039arXiv1312.1618OpenAlexW1965912522MaRDI QIDQ479279

Rodrigo Gondim, Francesco Russo

Publication date: 5 December 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1618

zbMATH Keywords

classificationconepolynomialssingularityLegendre transformcubic hypersurfacesstandard formhomogeneous Monge-Ampre equations.

Mathematics Subject Classification ID

Hypersurfaces and algebraic geometry (14J70) Projective and enumerative algebraic geometry (14N99) Polynomial solutions to PDEs (35C11)

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Cites Work

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• On degenerate secant and tangential varieties and local differential geometry
• Su certe forme a hessiana indeterminata
• Special linear systems and syzygies
• Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
• A geometrical approach to Gordan-Noether's and Franchetta's contributions to a question posed by Hesse
• Differential geometry of varieties with degenerate Gauss maps
• Smooth lines on projective planes over two-dimensional algebras and submanifolds with degenerate Gauss maps
• When does the Hessian determinant vanish identically? (On Gordan and Noether's proof of Hesse's claim)
• Classical Algebraic Geometry
• Bertini Forms and Hessian Matrices

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