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Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture |
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| Authors: | A Abdesselam J Chipalkatti |
| Institution: | a Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver BC V6T 1Z2, Canada b Department of Mathematics, University of Manitoba, 433 Machray Hall, Winnipeg MB R3T 2N2, Canada |
| Abstract: | The hypersurfaces of degree d in the projective space Pn correspond to points of PN, where  . Now assume d=2e is even, and let X(n,d)⊆PN denote the subvariety of two e-fold hyperplanes. We exhibit an upper bound on the Castelnuovo regularity of the ideal of X(n,d), and show that this variety is r-normal for r?2. The latter result is representation-theoretic, and says that a certain GLn+1-equivariant morphismSr(S2e(Cn+1))→S2(Sre(Cn+1)) |
| Keywords: | 05A15 14F17 20G05 81T18 |
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