Cook the pasta according to the package directions. Drain.
Meanwhile, heat the oil in a large skillet over medium-high heat.
Add the leeks, garlic, ½ teaspoon salt, and ¼ teaspoon pepper. Cook, stirring occasionally, until tender, 3 to 4 minutes.
Add the corn and wine. Simmer until the corn is tender, 2 to 3 minutes. Stir in the cream.
Add the pasta, season with ½ teaspoon salt and ¼ teaspoon pepper, and toss to combine. Fold in the arugula. Sprinkle with the pecorino before serving.