Well, there's really not a Vivaldi "piccolo" piece. It was probably originally written for recorder, but is often played on piccolo, earning it the title of a "piccolo concerto." If it's the piece I'm thinking of (there are actually several Vivaldi concerti played regularly on the flute/picc), the full title would be "Concerto (per flautino) in C Major, RV 443." Note that the "per flautino" is in parenthesis, because it often is omitted from the title.