This paper deals with two families of algebraic varieties arising from applications. First, the k-factor model in statistics, consisting of n-times-n covariance matrices of n observed Gaussian variables that are pairwise independent given k hidden Gaussian variables. Second, chirality varieties inspired by applications in chemistry. A point in such a chirality variety records chirality measurements of all k-subsets among an n-set of ligands. Both classes of varieties are given by a parameterisation, while for applications having polynomial equations would be desirable. For instance, such equations could be used to test whether a given point lies in the variety. We prove that in a precise sense, which is different for the two classes of varieties, these equations are finitely characterisable when k is fixed and n grows.
Additional Metadata
Keywords algebraic factor analysis, Noetherianity
MSC Toric varieties, Newton polyhedra (msc 14M25), Polytopes and polyhedra (msc 52Bxx), Representation theory (msc 20G05)
THEME Logistics (theme 3)
Publisher Academic Press
Journal Advances in Mathematics
Note (Link is to arxiv preprint.)
Draisma, J. (2010). Finiteness for the k-factor model and chirality varieties. Advances in Mathematics, 223(0811.3503), 243–256.