Corbett has edited the letters of James Schuyler and published two memoirs: Philip Guston’s Late Work: A Memoir (1994) and Furthering My Education (1997). He writes frequently on art, and in 1999 published a book on the sculptor John Raimondi. Corbett has served as a teacher in the Expository Writing program at Harvard University and as Writer-in-Residence in the Program of Writing and Humanistic Studies at Massachusetts Institute of Technology (MIT). He edits for the small publisher Pressed Wafer, which specializes in poetry broadsides, chapbooks and books.