Eva Hesse: Studiowork, Fruitmarket Gallery, Edinburgh

The legacy of a life cut short – works as frail as their creator and miracles of survival

It's hard to unpick Eva Hesse's biography from her work, even though auteurs have been out of fashion for 30 years now. The facts of her life, often rehearsed, are these.

Hesse was born in Hamburg in 1936 to a family of observant Jews. At two, she was put on a Kindertransport, first to Holland, then England and finally, in 1939, to America. Thirty years later, in New York, she was diagnosed with the brain tumour from which she died, aged 34. Her career as an artist had lasted 10 years. Threatened from the start, Hesse's short life was always tenuous. And it's difficult to feel that this tenuousness isn't echoed in the fascination of her work with the overlooked and hardly touched – with shreds of cloth and bits of paper so lightly handled that, like Hesse herself, they seem hardly to exist.

A problem with museums and galleries is that objects shown in them are lent automatic solidity. This has always been troublesome for Hesse, whose work, although dealing in increments of fragility, is sometimes large scale. And if this is true of her finished sculptures, then it is even more so of Hesse's so-called test pieces or sub-objects, the subject of a major Edinburgh Festival show.

When Hesse died in 1970, she left a studio full of these – experiments, maquettes, doodles in three dimensions. Or were they? Posterity confers value backwards. Because these objects haven't been shown in public – most were given to the Berkeley Art Museum by Hesse's sister – we see them as somehow lesser. This was certainly the experience of the artist's friend Sol LeWitt, who, pondering the studioworks at Berkeley a decade after Hesse's death, struggled to distinguish between those that were "definitely not pieces" and those that were; between "studio leavings" and sculpture proper.

You can see the problem. If a single word hangs over the Fruitmarket show, it is "fugitive" – perhaps applied to Hesse herself, but more literally so to her work. Hesse's sculptures have always been a conservator's nightmare, their media – meltable wax, yellowing latex, skeins of perishable cloth – apparently in love with their own mortality. Far from disguising its frailty, her work owns up to it: some of the latex pieces in the vitrines in the Fruitmarket's lower gallery seem to be rotting and, in a way, they are. In their carnality – one looks like burned flesh, another sprouts plastic hair – they have the feel of pathology samples, small elisions of sex and death.

As often – as always – the watchword here is context. If the key to Hesse's greatness (and that's not too big a word) is her grasp of the ephemeral, then these studioworks are the most Hesse-ish works of all. To her feel for the perishability of materials and genius for minimal intervention are added the objects' particular history. Like Hesse herself, the test pieces – if that is what they are – have struggled to exist. While her works in the Tate or Whitney are given gravitas by being where they are, most of these small objects come from private collections or the Berkeley archive. They could so easily have been thrown away; as LeWitt's indecision over them suggests, their status as artworks is far from secure.

And that, perhaps, is the problem. This is a hugely important show, bringing to life a lost part of Hesse's oeuvre. And yet the very act of museologising these objects means that they become the kind of works we find in museums. Seeing them in Hesse's studio (or even in the Berkeley's store room) is one thing; seeing them here is quite another. By asking the question, "Are these artworks?" – a question at the heart of their aesthetic – the Fruitmarket's show cannot help but answer it.

And so, being the clever show it is, it owns up to the problem. While the objects downstairs are exhibited in typically museological vitrines or frames, the ones upstairs are simply hung on the wall or left, unguarded, on a shelf. It is a high-risk strategy. The works on the shelf are made of papier mâché, in some cases moulded around a balloon. Two bowl-shaped pieces are from the same moulding: such is the fragility of their history that this became clear only when they were reunited here in Edinburgh for the first time in 40 years. They have weathered those years differently, ending up as dissimilar shapes and colours; a child's fingers would smash them in a trice. But it's the only way of showing them, really, if we are to see them for what they are.

Fruitmarket Gallery (0131-225 2383) to 25 Oct