Hi Fred,
You can email me directly if want more details about germination. It depends on the species is the best answer! The alternate temperate species of sect. Polygonatum require a minimum of 30 days cold, but need a warm period after that and then cold again, before producing a leaf. Species of sect. Verticillata vary with the alpine or high elevation verticillate-leaved species typically needing the above treatment, but some small percentage will germinate immediately and produce a leaf. Species in series Punctata and series Oppositifolia mostly are immediate epigeal, but cathcartii has a double dormancy. Series Grandiflora (huanum, kingianum, et al.) are immediate hypogeal with some immediate epigeal. The only species in sect. Sibirica, P. sibiricum, is double dormant.
The related Disporopsis is immediate epigeal and Heteropolygonatum seems to behave as double dormant for the few seeds I've been fortunate to be able to try.