Peel the pears, leaving the stems intact. Slice off a tiny bit of the bottom of each pear to help them stand upright.
To a small saucepan, add the wine, water, orange peel, orange juice, sugar, cinnamon stick and ginger slices. Bring the mixture to a boil over medium-high heat, stirring until the sugar is dissolved.
Carefully place the pears into the liquid and reduce the heat to a simmer. Cover the pan and cook for 15 to 25 minutes, or until the pears can be just pierced with a fork.
Gently remove the pears using a slotted spoon and set aside. Increase the heat to high, and cook until the poaching liquid reduces and turns a bit syrupy but not brown in color, about 15-20 minutes. Remove from the heat and discard the orange peel, ginger slices, and cinnamon stick.
To serve, slice the cooled pears into wedges. Pour a bit of the poaching syrup on top of the pears and/or directly onto the cheesecake. Serve the pears on top of the cheesecake.