Under English Common Law, the test of obscenity was defined as the tendency of the written matter to "deprave and corrupt those whose minds are open to such immoral influences, and into whose hands a publication of this sort may fall." In the United States, the issue of obscenity did not occupy much time for the national government. But the U.S. Supreme Court's occupation with the issue of obscenity began in the late 1950's. The Court has held the obscenity means more than basic vulgarity. TO be obscene, an expression must be erotic. Cohen v. California (1971) In 1985, the Court found it necessary to distinguish between lust, which it called a normal sexual response, and the categories of lasciviousness or prurient interest that involve a morbid interest in sex. Brockett v. Spokane (1985) If the activity of publication in question violates this rule above, it may be classified as 'obscenity' and by regulated by the local. Because of the Roth v. United States (1957) ruling, obscenity is not within the areas of constitutionally protected speech or press. Also, to be classified as obscenity the material or exhibition must meet three standards. 1)Whether the average person applying contemporary community standards, would find that the work, taken as a whole, appeals to prurient interest; 2)whether the work or exhibition depicts of describes, in a patently offensive way, sexual conduct specificially defined by the applicable state law; and 3)whether the work, taken as a whole, lacks "serious literary, artistic, political, or scientific value." To be classified as obscenity and be able to be regulated by the local government, the work or exhibition must meet all three of this criteria. Miller v. California (1973)
So the local government can indeed regulate obscenity and there are three established and very specific guidelines as to what qualifies as obscenity.