Finiteness for the k-factor model and chirality varieties

Details Finiteness for the k-factor model and chirality varieties Finiteness for the k-factor model and chirality varieties

2008-11-21

arxiv.org/abs/0811.3503v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

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.

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