There are red faces these days in the Communist-run Tuscan city of Leghorn and in the hallowed halls of many Italian museums and university art departments because of a major, and somewhat grotesque, art hoax.

This summer, three Modigliani-style carvings were dredged out of a city canal, were widely acclaimed as some of the sculptures that legend says the artist discarded in 1909, and were then hurriedly incorporated into a retrospective at a small Leghorn museum to celebrate the centenary of the avant-garde sculptor and painter who died in 1920 at the age of 36.

Now, only two months later, it has been revealed that all the carvings are false. First, four nonartistic university students came forward to say that as a joke they had fabricated "Modi Two," the second of two heads fished out of Leghorn's "Royal Canal" July 24. Then several weeks ago a young anarchist Leghorn dockworker with a prison record announced he had made "Modi One" as well as a third head retrieved on Aug. 9.

The confessions were greeted at first with incredulity, with some museum officials and art historians insisting until the last that the sculptures had to be genuine.

But university students Francesco Ferrucci, Pietro Luiridiana, Michele Ghilarducci and Michele Genovesi -- who said they were aghast when the "Stone Head" they had thrown into the canal was taken as authentic -- provided photos and stone fragments as proof. In the face of ongoing skepticism, they appeared on nationwide television to use an electric drill, a screwdriver and a chisel to make another "Modigliani."

And if any doubters still remained, they probably were silenced when 29-year-old Angelo Froglia projected a 20-minute color videotape showing himself in the process of carving "Modi One" and "Modi Three" and "cooking" them to approximate the 75 years Modigliani's sculptures were said to have remained under water.

Froglia, a former drug addict who served three years in Italian maximum security prisons for his part in a 1978 terrorist raid on a right-wing trade union headquarters, is a dockworker in Leghorn seaport. He says he decided to make the heads to prove how public opinion can be manipulated and to test Italy's art critics.

It would appear that many top critics and art historians here failed the test. Vera Durbe, director of the Villa Maria Museum and curator of this summer's Modigliani exhibit, was last heard proclaiming that the university students were "liars" and that their televised carving was simply "a joke in bad taste." Her brother, Dario, who is director of the National Museum of Modern Art in Rome, this summer rushed into print a book on the heads in which he wrote that when the sculptures were extracted from the mud of the canal bottom, "I had no doubt, at the first sight of them, that I found myself before two sculptures of Amedeo Modigliani."

Cesare Brandi, one of Italy's best-noted art critics, has been quoted as saying, "They are rough drafts, but Modigliani rough drafts. Those two heads have an interior light, like a sightseer . . . Within those two rough stones there is a presage, there is a presence." And Michele Catugeri, a Tuscan art official, has been reported by the Italian press to have written in his diary after seeing the newly retrieved heads, "I felt close to Modigliani as if those stones had the power to put us into physical content and wipe out the 75 years dividing his bitter gesture from our joyous discovery."

The emotional climate in Leghorn no doubt had been set in part by Vera Durbe's success in convincing city officials to drag the "Royal Canal." She, and many others, believed in an old legend that says Modigliani, having decided in 1909 to return to Paris after three years in Leghorn, asked his friends, "What should I do with my stones?" and took them at their word when they suggested, "Dump them into the canal."

Dragging of the canal began in early July. The first two heads were brought up in a mechanical scoop on July 24 and the third head was retrieved on Aug. 9.

The hoax has thrown the Italian art world into confusion, and things are not much better for city officials.

Opposition leaders in Leghorn are now calling for the resignation of the city's Communist mayor and commissioner of culture, and the Vatican newspaper Osservatore Romano blasted the city's Communist leadership for damaging Italy's image.

But some have put the hoax to their advantage. Recently the Rome newspaper La Repubblica ran a full-page ad showing a sketch of one of the heads, a photo of an electric drill, and underneath the caption: "We can all be talented with a Black and Decker."