From Wikitree: His origins are not known. He has been reputed to be the son of Andrea Alberti, who is said to have been Secretary of the Treasury of the Ducal Palace in Venice, and his wife Veronica Medici, aka Lady Veronica Cremona. There is no known basis for this identification. There is a record from Venice of a son named Giulio Caesari, born to Adrea Alberti and his wife Veronica in Venice and baptized there on 10 June 1608.[1] Some Internet sources claim that the child Giulio Caesari baptized in 1608 was Pietro, but this is not plausible.
From Wipedia: There is no evidence for the former assertion that Pietro was the son of the Secretary of the Ducal Treasury, Andrea Alberti and his wife, Lady Veronica Cremona... Their son was Giulio Cesare Alberti, not Pietro. A century ago a genealogist made the claim that they were the same person, but Giulio Cesare Alberti had a long career in the Venetian secretarial service, like his father. He served as secretary to the ambassador to Constantinople during the 1640s, became secretary to the Council of Ten (the second highest post a non-noble could achieve in Venice), never married, and died fabulously wealthy in Venice in 1686. His will and some of his letters to Venice from Constantinople have survived.
I have therefore disconnected Pietro Cesare Alberto from Andrea Piero Alberti and Lady Veronica Alberti, dei Cremona
Sincerely,
Tamas Caldwell-Gilbert