Projective Surface Automorphisms of Positive Topological Entropy from an Arithmetic Viewpoint
نویسنده
چکیده
Let X be a smooth projective surface over a number field K(⊂ C), and f : X → X an automorphism of positive topological entropy. In this paper, we show that there are only finitely many f -periodic curves on X . Then we define a height function ĥD corresponding to a certain nef and big R-divisor D on X and transforming well relative to f , and deduce some arithmetic properties of f -periodic points and non f -periodic points.
منابع مشابه
Automorphisms of Hyperkähler Manifolds in the View of Topological Entropy
First we show that any group of automorphisms of null-entropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. We then characterize automorphisms of a K3 surface with nullentropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.
متن کاملENTROPY OF GEODESIC FLOWS ON SUBSPACES OF HECKE SURFACE WITH ARITHMETIC CODE
There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...
متن کاملAutomorphisms of Rational Manifolds of Positive Entropy with Siegel Disks
Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.
متن کاملOD-characterization of $U_3(9)$ and its group of automorphisms
Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
متن کامل2 7 Fe b 20 09 Continuous Families of Rational Surface Automorphisms with Positive Entropy Eric Bedford
§0. Introduction. Cantat [C1] has shown that if a compact projective surface carries an automorphism of positive entropy, then it has a minimal model which is either a torus, K3, or rational (or a quotient of one of these). It has seemed that rational surfaces which carry automorphisms of positive entropy are relatively rare. Indeed, the first infinite family of such rational surfaces was found...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005