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After a cyclamen blooms, it will go into a dormant state. Going into a dormant state looks very much like the plant is dying, as the leaves will turn yellow and fall off. It is not dead, just sleeping. With proper cyclamen plant care, you can help it through its dormancy and it will rebloom in a few months.

When taking care of a cyclamen after blooming, allow the leaves to die and stop watering the plant once you see the signs that the leaves are dying. Place the plant in a cool, somewhat dark place. You can remove any dead foliage, if you would like. Let sit for two months.

For more information on the care of cyclamen, please visit the following link:
https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

A cool location is important to the health of a Cyclamen. A good trick is to enjoy the plant on a table during the day, away from direct sunlight and then tuck it into a cool room for the evening.

https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

Here is an article on the care and planting of Hardy Cyclamen.

https://www.gardeningknowhow.com/houseplants/cyclamen/hardy-cyclamen-outdoors.htm

This is generally the signal that you should stop watering the plant and let the plant go dormant for a period, usually following it's blooming period.
Here is a link with more information.

https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

It is best to remove the entire flower stem after is has faded.
Gently snip out the stem with a small garden scissors or a knife.

https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

There are about 20 species within the genus of Cyclamen.

This article has more information.

https://www.gardeningknowhow.com/houseplants/cyclamen/types-of-cyclamen-plants.htm