Heat oil in a 5 to 6 quart heavy pot over moderate heat until hot but not smoking, then cook onion,jalapeno, salt, and pepper, stirring occasionally, until onion is pale golden, about 8 minutes.
Meanwhile, peel potatoes and cut into 1-inch pieces.
Add broth, water, and potatoes to onion mixture and cover pot, then bring to a boil over high heat.
Reduce heat and simmer, uncovered, stirring occasionally, until potatoes are very tender, 12 to 14 minutes.
Coarsely mash potatoes in pot with a potato masher. Stir in corn and simmer, uncovered, 3 minutes.