In a saucepan over medium heat, heat the sugar with the water until the water boils and the sugar melts. Add the corn syrup, pomegranate juice, lemon juice and tangerine juice and simmer for 5 minutes.
Pour the mixture into a heatproof bowl, cool completely, cover and chill until completely cold.
Churn the pomegranate mixture in an ice cream maker according the manufacturer’s instructions.
Chill the sorbet in the freezer in the airtight container for at least 12 hours.