A Geometrical approach to Gordan-Noether's and Franchetta's contributions to a question posed by Hesse

被引：14

作者：

Garbagnati, Alice ^{[1
]}

Repetto, Flavia ^{[2
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

[2] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

COLLECTANEA MATHEMATICA | 2009年 / 60卷 / 01期

关键词：

Cones; vanishing hessian; dual varieties;

D O I：

10.1007/BF03191214

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Hesse claimed in [7] (and later also in [8]) that an irreducible projective hypersurface in P-n defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved in [6] that this is true for n <= 3 and constructed counterexamples for every n >= 4. Gordan and Noether and Franchetta gave classification of hypersurfaces in P-4 with vanishing hessian and which are not cones, see [6, 5]. Here we translate in geometric terms Gordan and Noether approach, providing direct geometrical proofs, of these results.

引用

页码：27 / 41

页数：15

共 14 条

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