They are indeed perennials. However there are only two which are truly hardy C. hederifolium, flowering now and C. coum which flower in late Winter. There are about 17 species at present.
The one which is sold for winter baskets is a form of C persicum, hardy only to about 5c.

Scylsium and Perperesene are also fully hardy...

I hope you mean C. cilicium and C. purpurascens. they may be hardy with you, but they died off here in what for us is a normal winter.
C. repandum might be, but never been able to get it to try.
C. alpinum might also be hardy, but again not tried it outside here.

Yes Owdb. typos both! We generally stick to coum and hederifolium, but the books do claim the other two are fully hardy...

Hi Nellie,
The dictionary definition says 'the corm is a rounded thick underground plant stem base with buds and scaly leaves that stores food and produces new shoots each year, similar to a bulb or tuber.'
I hope this answers your question

The ones Owdboggy mentioned sold for baskets about now are usually much brighter and showier than coum and hederifolium so you can easily tell the difference.

Some of the 'tender' ones have beautiful leaf patterns and, with diligence Bulba and I have managed to get them through couple of winters... you plant them up in a trough and move the whole thing into a cool front porch/ conservatory/green house the emphasis is 'cool'!