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摘要翻译：
Hesse认为，由hessian行列式消失的方程定义的不可约射影超曲面必然是锥。Gordan和Noether证明了对于$n\leq3$，这是正确的，并且对于每$n\geq4$，构造了反例。Gordan和Noether和Franchetta给出了$\pp^4$中的hessian消失且不是锥的超曲面的分类。这里我们用几何术语来翻译Gordan和Noether方法，提供这些结果的直接几何证明。
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英文标题：
《A geometrical approach to Gordan--Noether's and Franchetta's
contributions to a question posed by Hesse》
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作者：
Alice Garbagnati, Flavia Repetto
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Hesse claimed that an irreducible projective hypersurface in $\PP^n$ defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved that this is true for $n\leq 3$ and constructed counterexamples for every $n\geq 4$. Gordan and Noether and Franchetta gave classification of hypersurfaces in $\PP^4$ with vanishing hessian and which are not cones. Here we translate in geometric terms Gordan and Noether approach, providing direct geometrical proofs of these results.
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PDF链接：
https://arxiv.org/pdf/0802.0959
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