Pineapple in Ginger Rum Syrup

Bring water, sugar, and ginger to a boil in a wide 6-quart heavy pot, stirring until sugar is dissolved, then boil, uncovered, 3 minutes. Remove from heat and let syrup steep, covered, 10 minutes. Remove ginger with a slotted spoon and discard. Add pineapple to syrup and simmer, covered, stirring occasionally, until pineapple is translucent, 6 to 8 minutes. Transfer pineapple with slotted spoon to a heatproof bowl, then boil syrup, uncovered, until reduced to 2 cups, 10 to 15 minutes. Add rum to syrup and gently boil 1 minute, then pour over pineapple. Cool to room temperature, about 45 minutes. Serve at room temperature or chilled. Pineapple in syrup can be made 1 day ahead and chilled, covered.