A characterization of locally finite congruence modular varieties with the number of at most k-generated models being bounded from above by a polynomial in k is given. These are exactly the varieties polynomially equivalent to the varieties of unitary modules over a finite ring of finite representation type.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-3,
author = {Pawe\l\ M. Idziak and Ralph McKenzie},
title = {Varieties with polynomially many models, I},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {53-68},
zbl = {1002.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-3}
}
Paweł M. Idziak; Ralph McKenzie. Varieties with polynomially many models, I. Fundamenta Mathematicae, Tome 167 (2001) pp. 53-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-3/