2012/03/21 by Abdelmalek Abdesselam, Jaydeep Chipalkatti
Computer Science · Mathematics · #Class (philosophy) #Covariant transformation #Divisor (algebraic geometry) #Embedding #Ideal (ethics) #Mathematical Analysis and Transform Methods #Medical Image Segmentation Techniques #Tensor decomposition and applications #Triviality #Variety (cybernetics) #math.AG #math.RT #msc:13A50 #msc:14L30
paper · pdf · doi:10.4153/cjm-2012-046-1
published in Canadian Journal of Mathematics 66(1), 3-30 (Cambridge University Press) · 27 pages
arxiv created 2012/03/21 · openalex publication_date 2012/09/09 · openalex created_date 2016/06/24 · arxiv updated 2019/08/15 · openalex updated_date 2026/08/05
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.