Bud, your right that standing on singletrack is the best way to go fast but IMO its not in the corners. The exact reason you go faster in the straights is what hurts you in the turns. Standing on the pegs lightens the bike and allows it to flow under you. If you do this when cornering the bike is light as Fred explains. If the corner is an easy, sweeping corner, stay standing and turn the bike under you. If its a tight or rutted corner Your technique hurts you more than it helps, sit and take the corner then stand back up when you exit the corner.
On tight corners in the woods, I turn with the back wheel, i.e. brake sliding. Its really popular here in the US but not outside.
Good luck