Alex Rodriguez showed off his swanky new Miami mansion during Art Basel this week by putting on a show of work by hot New York painter-sculptor Nate Lowman — in his new indoor batting cage. A-Rod hung Lowman’s hip work in the net-lined cage installed inside the bachelor digs where he can practice his swing in privacy. The Yankee slugger invited a mix of stars and art collectors — including Owen Wilson, Val Kilmer, Peter Brant and Jane Holzer — to view Lowman’s work Wednesday. A source said, “Alex became more interested in collecting art after building the house and was introduced to Lowman. The event was also an unofficial housewarming, and many of the guests were talking about how amazing his house was. It’s very modern, sleek and minimal, with few personal possessions on show, apart from a giant Atari Pac-Man console and a jet ski on the deck.” A-Rod will even offer private viewings of his unusual gallery by appointment during Art Basel, which runs through Sunday.