Fixed Points of Smooth Varieties with Kodaira Dimension Zero
نویسنده
چکیده
Motivated by the above problems, we now turn to the results of this paper. We first look at the case when A is an abelian variety and φ : A → A is an endomorphism satisfying a mild polarization hypothesis. In this setting we are able to prove that #Fix(φl) grows exponentially as a function of l. More preciesely, let Ai be a simple abelian subvariety of A of dimension gi for i = 1, . . . ,m. Suppose that for each Ai there exists an ample line bundle Li on Ai such that φLi L ⊗qi i for some qi > 1 and φ(Ai) = Ai. In this case we are able to prove:
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