What does quadruvium mean in Latin?

quadruvium, a noun, means “crossroads; the quadrivium (four mathematical arts of arithmetic, geometry, music and astronomy)”.

What is the genitive of quadruvium?

The genitive singular is quadruviī. quadruvium is neuter, second declension.

noun · neutersecond declension

quadruvium n (genitive quadruviī or quadruvī)

neutercrossroads
De pauperibus in plateis vel in quadruviis iacentibus, ut ad ecclesiam veniant, et illorum confessiones donent.789 CE, Charlemagne, Capitulare generale (An. 789)
neuterthe quadrivium (four mathematical arts of arithmetic, geometry, music and astronomy)