To much of America, Rudy Giuliani is a genuine hero, but not to his ex-wife or their children. So which images will have more power? America’s Mayor or Broadway Rudy? The Faithful Leader or The Unfaithful Husband? The Able Manager or The Absent Dad?

Many contradictions are clouding Giuliani’s quest for the Republican nomination. This is a man of enormous strengths and serious flaws, a modern-day version of an ancient Greek hero, thunderous in battle and yet plagued by an Achilles ego.

The smart political money still believes that Giuliani’s negatives will outweigh his positives, that the flaws will prove fatal before he reaches the Oval Office. But firm predictions are foolish and outside events could clear his path.

Rudy faces a weak field, and his Republican rivals could knock each other off, much the way Dick Gephardt and Howard Dean did in 2004, opening the Democratic nomination for John Kerry. Another terrorist attack could forcefully remind voters of Rudy’s shining hour, his courageous response to Sept. 11.

And in truth, Giuliani possesses the one quality that Americans always look for in a president, executive experience, the habit of command. Lawmakers never run anything, which is why they generally make terrible candidates. They are also based in Washington, another huge handicap. Rudy’s home river is the Hudson, not the Potomac.