On the theory of Gordan-Noether on homogeneous forms with zero Hessian (Improved Version). (English) Zbl 1455.14118
Kuroda, Shigeru (ed.) et al., Polynomial rings and affine algebraic geometry. Selected papers based on the presentations at the conference, PRAAG 2018, Tokyo, Japan, February 12–16, 2018. Cham: Springer. Springer Proc. Math. Stat. 319, 73-107 (2020).
Summary: We give a detailed proof for P. Gordan and M. Nöther’s results in [Math. Ann. 10, 547–568 (1876; JFM 08.0064.05)]. In [Bull. Braz. Math. Soc. (N.S.) 35, No. 1, 71–82 (2004; Zbl 1061.12002)], C. Lossen has written a paper in a similar direction as the present paper, but did not provide a proof for every result. In our paper, every result is proved. Furthermore, our paper is independent of Lossen’s paper and includes a considerable number of new observations.
For the entire collection see [Zbl 1458.13002].
For the entire collection see [Zbl 1458.13002].
MSC:
| 14R05 | Classification of affine varieties |
| 14J70 | Hypersurfaces and algebraic geometry |
| 14R10 | Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) |
| 13A50 | Actions of groups on commutative rings; invariant theory |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
References:
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