7 citations · 7 across the 2 of their papers we have counts for
5 papers
Canonical height functions on the affine plane associated with polynomial automorphisms
Shu Kawaguchi
Let be a polynomial automorphism of dynamical degree over a number field . (This is equivalent to say that is a polynomial autom…
Canonical heights, invariant currents, and dynamical systems of morphisms associated with line bundles
Shu Kawaguchi
We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their propertie…
A remark on periodic points on varieties over a field of finite type over Q
Shu Kawaguchi
Let M be a field of finite type over {\bf Q} and X a variety defined over M. We study when the set {P \in X(K) \mid f^{\circ n} (P) = P for some n \geq 1} is finite for any finite…
Height and Intersection for a family of semi-stable curves
Shu Kawaguchi
In this paper, we consider an arithmetic Hodge index theorem for a family of semi-stable curves f: X \to B with f_{\bf C} being smooth, generalizing Faltings-Hriljac's arithmetic H…
Inequalities for semistable families of arithmetic varieties
Shu Kawaguchi, Atsushi Moriwaki
In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that…