In a saucepan, combine the sugar and water and bring to a boil, stirring until the sugar dissolves. Let cool.
In a small saucepan, bring the tequila to a boil. Cook until reduced by half (most of the alcohol will boil off), about 10 minutes. Pour the tequila into a bowl and stir in the cooled sugar syrup, the lime juice, Triple Sec, corn syrup, and water.
Pour the chilled mixture into an ice-cream maker and process following the manufacturer’s instructions. Store, covered tightly, in the freezer.
For a granita-style dessert, pour the mixture into a shallow container. Freeze until a fair amount of ice crystals form, about 1 hour, and then stir vigorously with a fork to break them up. Repeat freezing and stirring every hour or so until the mixture is thoroughly frozen but slightly slushy, about 6 hours. Then allow the granita to freeze completely.