Also, is it a noun or an adjective? What's the nominative? (moved second question here)
Sorry, I'm a total n00b and checked all sorts of declension tables but I just can't figure this one out.
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Venetiarum is the genitive plural of the first-declension noun Venetia, -ae. Venetiae, -arum (plural) is Latin for English Venice (singular).
Patriarchatus Venetiarum thus means "The Patriarchate of Venice."
Why is Venetiae plural? We have a parallel situation in English, since we refer to one country as "The Maldives" (plural). The plural refers in both cases to a group of islands classed as one territory.
My translation of Carl von Czoernig's Die alten Völker Oberitaliens:
Since the time of Constantine, this country was no longer called Venetia but Venetiae in the plural, because of the distinction between Venetia superior and inferior; in all likelihood the former comprised the mainland area and the latter included the area along the lagoon. The latter was also already in Roman times called Venetia marittima. During the time that the Goths, Longabards, and Franks ruled, this country was also called Venetiae, -arum in the plural. (pg. 125)