On Hermite's invariant for binary quintics

JOURNAL OF ALGEBRA

卷:317

Article

Chipalkatti, Jaydeep

关键词: classical invariant theory;    covariant;    evectant;    Hermite invariant;    Hilbert-Burch theorem;    involution;    Morley form;    transvectant;   

DOI  :  10.1016/j.jalgebra.2007.06.021

来源: Elsevier

【 摘 要 】

Let H subset of P-5 denote the hypersurface of binary quintics in involution, with defining equation given by the Hermite invariant H. In Section 2 we find the singular locus of R, and show that it is a complete intersection of a linear covariant of quintics. In Section 3 we show that 7-l is canonically isomorphic to its own projective dual via an involution. The Jacobian ideal of H is shown to be perfect of height two in Section 4, moreover we describe its SL2-equivariant minimal free resolution. The last section develops a general formalism for evectants of covariants of binary forms, which is then used to calculate the evectant of H. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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