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arXiv · 1203.4761

On Hilbert covariants

Abdelmalek Abdesselam·Jaydeep Chipalkatti
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Abstract

Let F denote a binary form of order d over the complex numbers. If r is a divisor of d, then the Hilbert covariant H_{r,d}(F) vanishes exactly when F is the perfect power of an order r form. In geometric terms, the coefficients of H give defining equations for the image variety X of an embedding P^r->P^d. In this paper we describe a new construction of the Hilbert covariant; and simultaneously situate it into a wider class of covariants called the Göttingen covariants, all of which vanish on X. We prove that the ideal generated by the coefficients of H defines X as a scheme. Finally, we exhibit a generalisation of the Göttingen covariants to n-ary forms using the classical Clebsch transfer principle.

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Abdelmalek Abdesselam, Jaydeep Chipalkatti. 2012-03-21. On Hilbert covariants. https://doi.org/10.4153/cjm-2012-046-1

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