The holiday season is booming here, and much of the action is swirling around Lincoln Center, where shows of all sorts are jostling for space. The buildings might seem crowded if one attraction - the Big Apple Circus - didn't prefer setting up quarters in its own tent.
The prima donna of Lincoln Center at Christmastime is, predictably, the New York City Ballet's annual production of ''The Nutcracker.'' This year's edition, running through Jan. 2 at the New York State Theater, finds the spectacle in full bloom, as dazzling to the eye as anything I've seen on a stage.
It's hard to avoid a cliche like ''sheer magic'' when describing the first act, with its old-fashioned story decked out in high-tech lighting and visual effects, culminating in a ''Dance of the Snowflakes'' amid an elaborate onstage blizzard. Act II is more modest, physically, though more sophisticated in its dancing. In short, it's a rousing evening, and my children enjoyed it almost as much as I did, though they disagreed on which of the two acts was more fun.
A less expensive attraction - in fact, it's free - is the 12th annual Community Holiday Festival. It continues through Jan. 4 at Lincoln Center, and features a series of children's matinees as well as family shows in the evening. The performers come from New York City's five boroughs and nearby Westchester County, presenting programs of music, theater, and dance.
This year's matinee series features the Iron Clad Agreement theater company, whose production of ''Thomas A. Edison'' depicts the inventor as he creates the lightbulb, the record player, and the movie camera. And the audience gets to participate.
The festival's family portion opens the day after Christmas with a ''Salute to the Arts and Culture That Began in Harlem,'' presented by the Harlem Cultural Council.