MAYOR ANTONIO VILLARAIGOSA strode in front of a dozen cameras on Monday to discuss a very personal matter: the collapse of his marriage to Corina Villaraigosa. So perhaps it was inevitable that the first question out of a reporter’s mouth brought the whole thing to a screeching halt.

The question, of course, was this: Did Villaraigosa have an extramarital affair — KNBC-4’s Laurel Erickson delicately termed it a romantic relationship — during the course of his two-year-old mayoral administration? And if so, will such a relationship come out in the open now that Villaraigosa is transitioning publicly out of his 20-year marriage?

Anyone intimately familiar with the mayor has been asking those questions for months, ever since Villaraigosa confirmed to an unnamed Los Angeles Times reporter, in a story buried deep, deep within the newspaper, that the marriage was under strain. When Erickson brought the question out into the open, he described it as off-limits. “Let me just say that I made it absolutely clear: This is a private matter,” he tersely replied. “It’s a matter between me and my family. Those kinds of questions are inappropriate and I won’t answer them.”

But if the matter is so private, why summon reporters to City Hall to discuss the marriage in the first place? After all, the mayor seemed to have gotten away scot-free on Friday, the day his office put out a terse three-paragraph press release announcing that he and Corina, a language specialist at Montebello Unified School District, had decided to live in separate homes.

With the loony Paris Hilton spectacle drowning out nearly every other piece of news, TV devoted just a few seconds to the mayor’s marital matter last week. But Villaraigosa, always eager to address the cameras, felt obligated to give everyone another bite of the apple, publicly opening the door to the very issues he then deemed private. With two television reporters broadcasting live for the 11:30 a.m. news, Villaraigosa stood at his lectern describing the end of his marriage as a personal failure. “It has been a stable kind of anchor for the family,” he declared.

Only a few weeks earlier, former Mayor Richard Riordan — L.A.’s mayor from 1993 to 2001 — surprised many insiders with his own written statement saying that he and his longtime wife, Nancy Daly Riordan, are separating, but citing no reasons. And four years ago, Mayor James Hahn sent out an equally brief press release announcing a separation from his wife, Monica Hahn.

In some ways, Villaraigosa was following in Hahn’s footsteps. Both men put out statements on their marriages halfway through their four-year terms, giving the public a full two years for the idea to sink in before the next election. Hahn, dogged by rumors about his own marriage, issued his statement in July 2003. Villaraigosa, the subject of whispered questions for months, settled for early June.

Both statements reached reporters in the late afternoon, forcing them to scramble. But Villaraigosa then took a different course, holding a press conference to declare that he takes responsibility for the demise of his marriage.

So since he brought it up and all, what is he taking responsibility for? On Friday, less than an hour after the press release went out, the Los Angeles Daily News Web site initially reported that the demands of Villaraigosa’s job had caused the couple to separate. Villaraigosa’s press staff quickly called the newspaper to correct the record, saying such an assertion is untrue. If they were willing to rule out his work as a cause, why not rule out the other possibilities?

Faced with the question about another romantic relationship, Villaraigosa shut down. “My family and I have the right during this difficult time to go through this process free of that kind of speculation,” he declared. But by refusing to answer the question, Villaraigosa was in fact fueling that speculation, which began months ago once eagle-eyed observers of city politics noticed that he’d stopped wearing his wedding ring. (Villaraigosa said it no longer fit because he had lost so much weight.)

Here’s why it matters: Four months ago, San Francisco Mayor Gavin Newsom announced that he had had his own affair. On its face, the notion of a side romance by a San Francisco mayor might seem like tame stuff. But Californians suddenly had a very different perspective on San Francisco’s mayor once they learned that Newsom had been seeing the wife of his longtime friend. In short, they got a fuller understanding of the man who represents them.

GOP presidential candidate Rudy Giuliani had his own messy divorce that resulted in terrible personal consequences for his family. Neither of his children are speaking to him, and Giuliani, in fact, did not speak to his daughter at her own high school graduation. We learned that because the New York Post reported on that event. Because of those reports, voters have a clearer understanding of Giuliani, a man known for freezing out those closest to him.

Villaraigosa’s only publicly known affair, spelled out in new detail in a recent New Yorker profile, described how, on the morning after his victory in a spring primary for a state Assembly seat in 1994, he disappeared for a few days with another woman, leaving his wife in the uncomfortable position of calling his political allies as she tried to locate her husband.

If Villaraigosa engaged in another extramarital affair, that relationship could be utterly mundane. But it could also involve a city commissioner or a city contractor, a lobbyist or a land-use lawyer, a reporter or a renters’-rights advocate. And if Villaraigosa has been seeing anyone whose work intersects with his public duties, then the public deserves to know.

Villaraigosa isn’t talking, however, leaving the public with tightly choreographed presentations. Los Angeles City Councilman Jack Weiss, the mayor’s closest ally at City Hall, called reporters on Friday to tell them that Villaraigosa and his wife deserve their privacy. Union leader Maria Elena Durazo, who experienced her own share of marital difficulties as the wife of the late labor powerhouse Miguel Contreras, described the couple as loving parents. On Monday, Villaraigosa aides said reporters would be allowed to ask exactly five questions.

Here’s what we know: Corina Villaraigosa filed for divorce in Los Angeles County Superior Court, citing “irreconcilable differences.” The separation will be the first time that the two will live apart during his time as mayor, according to Villaraigosa spokeswoman Janelle Erickson. For the time being, Villaraigosa will live at his hilltop home in Mount Washington, and his wife and two children at Getty House, the official mayor’s mansion in Windsor Square.

The long-term living arrangements haven’t been worked out. But Antonio Jr. is heading to Princeton University in the fall, while Natalia Fe is enrolled at the Marlborough School, a private school not far from the Getty House.

Everything else is, for now, a mystery, with the mayor portraying his very public persona as a private one. Villaraigosa is sealing off the details of his personal life, even as he presents messages about that personal life for public consumption. If nothing else, the whole thing has a dizzying circularity.

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