The bipartite Brill-Gordan locus and angular momentum

Details The bipartite Brill-Gordan locus and angular momentum The bipartite Brill-Gordan locus and angular momentum

2005-02-25

arxiv.org/abs/math/0502542v1

Mathematics

Algebraic Geometry

LaTeX, 37 pages

Scientific paper

This paper is a sequel to math.AG/0411110. Let P denote the projective space of degree d forms in n+1 variables. Let e denote an integer < d/2, and consider the subvariety X of forms which factor as L^{d-e} M^e for some linear forms L,M. In the language of our earlier paper, this is the Brill-Gordan locus associated to the partition (d-e,e). In this paper we calculate the Castelnuovo regularity of X precisely, and moreover show that X is r-normal for r at least 3. In the case of binary forms, we give a classical invariant-theoretic description of the defining equations of this locus in terms of covariants of d-ics. Modulo standard cohomological arguments, the proof crucially relies upon showing that certain 3j-symbols from the quantum theory of angular momentum are nonzero.

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