The Supreme Court's definition of obscenity (the so-called _Miller_
test) is:

1) must appeal to the prurient interest of the average person

2) must describe sexual conduct in a way that is "patently offensive"
to community standards

and

3) when taken as a whole, it "must lack serious literary, artistic,
political, or scientific value"

Note that only "patently offensiveness" is decided by community
standards.

greeny@top.cis.syr.edu (Jonathan Greenfield) adds:

[...]
It should also be noted that local community's do NOT have total control
over the definition of "patently offensive."

In the 1974 case of Jenkins v. Georgia the SC unanimously overturned an
Albany, Georgia's court decision that "Carnal Knowledge" (the highly-
acclaimed Jack Nicholson film from 1971) was obscene, in a decision that
"clarified" (modified) the 1973 decisions of Miller v. California and
Paris Adult Theatre v. Slaton.

In the court's opinion, Justice Rehnquist wrote, "it would be a serious
misunderstanding of Miller to conclude that juries have unbridled discretion
in determining what is 'patently offensive.'"

The opinion further stated the court's expectation that appelate courts,
would necessarily be needed to protect non-obscene material from local
communities attempting to ban it as obscene.

In a concurring decision, Brennan, Marshall, and Douglas (all of whom
dissented in the Miller case), renewed their argument that the standard
created by Miller ultimately left only the SC to make determinations of
what was obscene, and as such was completely impractical.