At the Vivian Beaumont Theater at Lincoln Center.
Tom Stoppard constructs an elaborate device for his new play ''Arcadia,'' which is receiving its American premiere at Lincoln Center. Set in the drawing room of a large country house, the play shifts back and forth in time from 1809 to the present, cleverly intersecting characters and situations to contrast and parallel its themes.
It's all very ingenious, and many people, starved for intellectual stimulation of any kind in the theater, have hailed it as a masterpiece. But the play, for all its elaborateness of structure, is an ultimately hollow exercise that had audience members all around me nodding off in their seats. See the play if you are interested in discursive references to landscape gardening, chaos theory, and Fermat's theorem, but don't expect to be moved.
In 1809, the house belongs to an upper-crust couple, the Crooms, whose daughter, Thomasina (Jennifer Dundas), is a precocious teenage math prodigy being tutored by Septimus (Billy Crudup). Septimus is a friend of Lord Byron, who occasionally visits (although not in the course of the play). Other guests include a landscape architect and an inferior poet whose wife has fallen prey to Septimus's charms.
In the present day, another generation of the same family, the Coverlys, inhabits the estate, including Valentine (Robert Sean Leonard), a young mathematician who discovers the extent of Thomasina's brilliance.
One of the themes of the play is the way in which we apply our expectations to historical scholarship, bending the results to fit our preconceived ideas. Thus, in the 1809 segment, we watch Thomasina idly draw a figure of a man on a painting in the sitting room, and in the present, art critic Hannah Jarvis (Blair Brown) is researching a book on the ''mysterious hermit'' in the picture. Another writer, Bernard Nightingale (Victor Garber), has elaborate and very wrong theories about the Lord Byron connection.
Eventually the characters of both eras cross over, and the stage is a dizzying confluence of past and present. We see how events of the past prefigure and influence the present, and it is all constructed with wit and imagination. But we get the main idea of the play early on, and the evening is largely one of repetition as we admire the way Stoppard performs variations on a theme. The characters, although they say amusing things, don't engage us, so we care little about Valentine's infatuation with Hannah or Thomasina's early death.
Trevor Nunn, who staged it in England, has given the evening a polished sheen that makes it all go down smoothly, and Mark Thompson's vertical set and elegant costumes make it a pleasure to look at. The acting is a mixed bag; Garber gives Nightingale an amusing campy edge, and Brown is all too effective at conveying her character's brittleness. Many of the others are less effective.
''Arcadia's'' benefits might be more readily attained by reading it. In its current staging, the play is easier to respect than to like.