The village of Scarsdale, N.Y., asked the Supreme Court yesterday to overturn a lower-court ruling that might require the predominantly Jewish suburb of New York City to erect a nativity scene in a public park.

Marvin Frankel, an attorney for Scarsdale, argued that the appeals court decision would require the village to allow displays of "swastikas, a Klan symbol, a hammer and sickle" and other "offensive" signs.

Marvin Schwartz, representing a group of churches, said the village could not allow some groups to use the park while denying it to other groups. The court is expected to rule this spring in Board of Trustees v. McCreary.

The Supreme Court also heard arguments yesterday involving the legal definition of "lust" and whether anything that "incites" lust can be banned as obscene.

The case involves a 1982 Washington state anti-obscenity law. The law, which has not been enforced, was challenged by booksellers who said it was unconstitutionally broad. A federal appeals court agreed.

Attorneys for the state said the law properly banned "offensive" books and movies and asked the high court to overturn the appeals court.

The cases are Eikenberry v. J-R Distributors and Brockett v. Spokane Arcades.

The court also ruled that:

* The Western Shoshone Indians had no legal claim to millions of acres of land in Nevada because the government had established a fund in 1979 to settle all claims. The case is U.S. v. Dann.

* A prosecutor's improper remarks to a jury, in response to improper goading by a defense lawyer, do not necessarily require a judge to throw out an otherwise lawful conviction. The case is U.S. v. Young.