Preheat oven to 400°F. Heat olive oil in a 10-inch cast-iron skillet. Add jalapeños, red pepper and corn and cook over moderate heat, stirring, until wilted, about 4 minutes. Scrape mixture onto a plate and let cool completely. Wipe out skillet with a paper towel.
Stir together sugar and water in a large bowl until sugar dissolves. Stir in vegetable oil. Sift together flour, cornmeal, baking powder and salt into a medium bowl. Beat dry ingredients into sugar mixture with an electric mixer. Add eggs and cooked vegetables and beat until just blended.
Scrape batter into cast-iron skillet and bake until golden brown and a cake tester inserted in the center comes out clean, about 30 minutes (if top browns too quickly, cover with foil). Serve cornbread warm.
