A study of compact complex manifolds admitting non-isomorphic surjective endomorphisms

点击翻译按钮获取中文摘要

We have studied structures of smooth projective 3-folds X with negative Kodaira dimension admitting non-isomorphic \'{e}tale endomorphisms. We can show that a suitable finite \'{e}tale covering X' of X is classified into 6 types. There exists some X where X' cannot be decomposed as a product of a uniruled surface and an elliptic curve. The contraction morphism associated to R is the inverse of a blow-up of another smooth 3-fold along an elliptic curve. The trouble is that R cannot necessarily be stabilized by a suitable power of f. Hence the minimal model program(MMP) cannot work so as to be compatible with endomorphisms. As a substitute, we consider the tower of non-isomorphic finite \'{e}tale covering of 3-folds (called ESP), on which MMP works well. Such a 3-fold X can be obtained as a succession of blow-ups along an elliptic curve from a characteristic ESP (called DESP). We can also give a simple criterion for certan conic bundles to have non-isomorphic \'{e}tale endomorphisms.