Karen Kilimnik

Nothing could be more recherché than painting, except perhaps ballet. This most precious of 19th-century art forms pirouettes through Karen Kilimnik's paintings like a clockwork doll that hasn't been played with for centuries and, newly discovered in the attic, suddenly begins its wooden dance through the cobwebs and dust. It speaks of memory, but what memory? And whose? There is autobiography in Kilimnik's art, but whether it is hers or a fictional character's is anyone's guess. Throughout this seductive show, the promise of intimacy and openness is constantly deferred. Her birth date in the catalogue entries varies between 1955 and 1962 and although her exhibition at the South London Gallery is dripping with Russian references, no one can confirm her Russian roots. One of her paintings is called Moscow (1999). Ostentatiously framed, it mimics the look of a pavement artist's landscape in broad pastel strokes. It depicts a view across the water at the Church of Our Saviour in Moscow, a vast onion-domed monstrosity, a pastiche reproduction of a Czarist church that was demolished by Stalin and has been recently remade at vast expense. In other words, it is a painting of a false memory.

Kilimnik comes on like a mysterious countess in a romantic novel, tantalising us with clues to her true identity, but always vanishing into the night when we believe we finally have her in our grasp. This show is filled with numerous red herrings and almost Baroque elaborations of identity. Huge satin ribbons are draped over closely hung paintings, the sound of ballet music fills the gallery, and in the middle of the floor is a flower-covered grave: it is Giselle's, the heroine of the ballet of the same name, a girl who goes mad and dies of grief when she discovers her lover is a fake. Several paintings pay tribute to Swan Lake (1877) and The Nutcracker (1892), while another alludes to the teen horror film The Craft (1997).

The ballet fan, the film fan and the pet lover who paints her dogs, cats and ghost horse, all supposedly represent the 'true' Kilimnik. Yet, if this exhibition is 'phoney as hell', as Jackson Pollock might have said, its theme is how painting 50 years after Pollock can still communicate directly from the heart. The hokiness of Kilimnik's painting makes explicit the hokiness of painting itself. To paint is to make an embarrassing claim to ownership of something that, with training, anyone might replicate. To make a distinctive mark on canvas is to make a claim to self-expression that is laughably easy to disprove. Kilimnik paints in a way that leaves the Expressionist fallacy looking especially fallacious. She adopts the manner of an adolescent or naive painter whose sense of originality is woefully at odds with its derivative technique. She paints like someone who thinks they are saying something unique when really they are just reworking the same ground generations of Sunday artists have gone over before. This would not, in itself, make her a very interesting painter, just another ironist, were it not for the utterly contradictory passion that informs her art. If her subject matter and borrowed brushstrokes are familiar, behind it all - the stories that don't add up, the affinities that aren't explained - is something very difficult to articulate, an experience, an autobiography, a world view, a private self. Take her portraits of pets, for example. Their searching eyes won't leave you alone. Here's her dog in the snow. Here's her cat Harlequin 'at the farm in Scotland, Halloween'. What farm in Scotland? Yet the animals' cute eyes and warm fur seem real enough, as does the love.

The Russia imagined in this exhibition is a Utopia of romantic feeling, a place where everyone listens intently to ballet music, speaks from the heart and departs on a sled. Kilimnik longs for such a place, as her own feelings keep coming out wrong. Can she really feel that much for a dog or a cat or Hugh Grant? There's nothing in the paintings to prove that she does, but behind the fictions of feeling there is the sense of real things and feelings which are difficult to express. Her stress on the obscure and the outmoded is in itself a confession of secrets. Kilimnik's affinity for ballet, painting and dolls coming to life under the Christmas tree suggests a hinterland, a secret space of memory, the equivalent of an attic stuffed with mouldering old toys. Perhaps the experience alluded to is that is that of exile, the migrant history narrated - or faked - in her Moscow painting. Or perhaps it is a more universal dispossession.