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When does the Hessian determinant vanish identically ? ( On Gordan and Noether ’ s Proof of Hesse ’ s Claim )
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lossen, Christoph |
| Copyright Year | 2004 |
| Abstract | In 1851, Hesse claimed that the Hessian determinant of a homogeneous polynomial f vanishes identically if and only if the projective hypersurface V (f ) is a cone. We follow the lines of the 1876 paper of Gordan and Noether to give a proof of Hesse's claim for curves and surfaces. For higher dimensional hypersurfaces, the claim is wrong in general. We review the construction of polynomials with vanishing Hessian determinant but V (f ) not being a cone. For three dimensional hypersurfaces the latter gives, again, the complete answer to the question asked in the title. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.emis.de/journals/em/docs/boletim/vol351/v35-1-a4-2004.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
