Battle lines have been drawn between competing asteroid projects. On Friday, Paramount and DreamWorks an-nounced an April 21 start date for ”Deep Impact,” which Mimi Leder will direct and David Brown and Richard Zanuck will produce (Daily Variety, Jan. 9). Meanwhile, Touchstone Pictures has targeted a May start for ”Armageddon,” which Michael Bay is sealing a deal to direct and produce with Gale Anne Hurd. Jonathan Hensleigh is rewriting the script by Robert Roy Pool. Both projects concern heavenly bodies on a collision course with Earth.