Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture

Details Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture

2004-11-05

arxiv.org/abs/math/0411110v1

Mathematics

Algebraic Geometry

This is a considerably expanded version of math.AG/0405236

Scientific paper

Combining a selection of tools from modern algebraic geometry, representation theory, the classical invariant theory of binary forms, together with explicit calculations with hypergeometric series and Feynman diagrams, we obtain the following interrelated results. A Castelnuovo-Mumford regularity bound and a projective normality result for the locus of hypersufaces that are equally supported on two hyperplanes. The surjectivity of an equivariant map between two plethystic compositions of symmetric powers; a statement which is reminiscent of the Foulkes-Howe conjecture. The nonvanishing of even transvectants of exact powers of generic binary forms. The nonvanishing of a collection of symmetric functions defined by sums over magic squares and transportation matrices with nonnegative integer entries. An explicit set of generators, in degree three, for the ideal of the coincident root locus of binary forms with only two roots of equal multiplicity.

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