Whip the cream and whisk with the mascarpone. The best way to do this is to break the mascarpone, i.e. beat it with an electric whisk until it becomes creamy and then gradually stir in the cream.
Halve the pomegranates and squeeze them, just like citrus fruits. Then strain through a sieve into a bowl. Squeeze the lime and add to the pomegranate juice. Add the powdered sugar to the juice mixture and stir in vigorously until the powdered sugar has dissolved. Now fold in the mascarpone cream mixture and then beat again with the electric whisk.
Fill the ice cream mass into flat, sealable plastic bowls and let freeze for at least 5 hours. I like to use several shallow bowls as the ice will freeze through more quickly. No stirring is necessary when freezing, as the ingredients do not form such large ice crystals. However, nothing speaks against preparation in the ice cream machine.
Let thaw for 15 minutes to serve and decorate with pomegranate seeds as desired.