Let X be a normal projective variety over an algebraically closed field k of characteristic 0. We consider an int-amplified surjective endomorphism f of X, that is f^*L - L =H  for some ample Cartier divisors L and H. In this talk, we’ll first give a rough characterization of X related to its singularities, canonical divisor, MRC fibration and Albanese map, etc. We’ll then show that one can run the minimal model program (MMP) f-equivariantly, after replacing f by a positive power, for a mildly singular X. Some applications will also be mentioned.

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