Kahler-Ricci flow on varieties of general type -- Gabriele LaNave

The Kahler-Ricci flow on a projective variety of general type would seem to be suitable for the metric study of the canonical model. One runs into problems in finite time if the canonical bundle is not nef, when the Kaheler-Ricci flow forces to cross the wall separating the big bundles from the ample ones. We will discuss the state of affairs for projective surfaces, and indicate some general results for higher dimensional varieties.