Another new book reminds us that Broadway and Hollywood have been carrying on an affair, set to music, since the 1920s. A Fine Romance: Hollywood/ Broadway is a lovingly produced celebration of the relationship that became a marriage. Darcie Denkert makes her case by devoting chapters to productions such as West Side Story, My Fair Lady, Cabaret and Chicago, tracing the various transformations from stage to screen. Case in point: Chicago, based on the sensational Jazz Murders of 1924, was first a 1926 play and then a silent film, and was remade in 1942. Jump to the '60s, and Bob Fosse's search for a production to feature Gwen Verdon. Thus, the Broadway musical. And finally, the Oscar-winning film of 2002.