Kaoru Sano

collaborators

5 papers

math.AG2026

On the height boundedness of periodic and preperiodic points of dominant rational self-maps on projective varieties

Yohsuke Matsuzawa, Kaoru Sano

We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. A…

math.CO2025

Rectangulations avoiding a pattern

Kaoru Sano

Fix a strong rectangulation pattern $P$ of size $L$ . We show that the growth constant of the class of strong rectangulations avoiding $P$ is strictly smaller than $I^ = 27/2$ , the gr…

math.NT2025

The number of rational iterated preimages of the origin under unicritical polynomial maps

Kaoru Sano

We study rational iterated preimages of the origin under unicritical maps $f_{d, c} (x) = x^{d} + c$ . Earlier works of Faber--Hutz--Stoll and Hutz--Hyde--Krause established finiteness and…

math.NT2025

Irreducibility of polynomials defining parabolic parameters of period 3

Junnosuke Koizumi, Yuya Murakami, Kaoru Sano +1

Morton and Vivaldi defined the polynomials whose roots are parabolic parameters for a one-parameter family of polynomial maps. We call these polynomials delta factors. They conject…

math.DS2025

Arithmetic properties of multiplier polynomials for certain polynomial maps

Yuya Murakami, Kaoru Sano, Kohei Takehira

We investigate the arithmetic properties of the multiplier polynomials for certain $1$ -parameter families of polynomials. In particular, we prove integrality theorems of multiplier…