S. Kuroda

activity

20072026

most citedWildness of polynomial automorphisms in three variables

10 citations · 21 across the 19 of their papers we have counts for

collaborators

Showing math.ACShow all

15 papers · 1 filter

math.AC2022

Polynomial automorphisms of characteristic order and their invariant rings

Shigeru Kuroda

Let $k$ be a field of characteristic $p > 0$ . We discuss the automorphisms of the polynomial ring $k [x_{1}, \dots, x_{n}]$ of order $p$ , or equivalently the $Z / p Z$ -actions on…

math.AC2021

A new class of finitely generated polynomial subalgebras without finite SAGBI bases

Shigeru Kuroda

The notion of initial ideal for an ideal of a polynomial ring appears in the theory of Gröbner basis. Similarly to the initial ideals, we can define the initial algebra for a subal…

math.AC2018

Hilbert's fourteenth problem and field modifications

Shigeru Kuroda

Let $k (x) = k (x_{1}, \dots, x_{n})$ be the rational function field, and $k ⫋ L ⫋ k (x)$ an intermediate field. Then, Hilbert's fourteenth problem asks whethe…

math.AC2016

The automorphism theorem and additive group actions on the affine plane

Shigeru Kuroda

Due to Rentschler, Miyanishi and Kojima, the invariant ring for a $G_{a}$ -action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we gi…

math.AC2016

Stably co-tame polynomial automorphisms over commutative rings

Shigeru Kuroda

We say that a polynomial automorphism $ϕ$ in $n$ variables is stably co-tame if the tame subgroup in $n$ variables is contained in the subgroup generated by $ϕ$ and affine automorp…

math.AC2014

A generalization of Nakai's theorem on locally finite iterative higher derivations

Shigeru Kuroda

Let $k$ be a field of arbitrary characteristic. Nakai (1978) proved a structure theorem for $k$ -domains admitting a nontrivial locally finite iterative higher derivation when $k$ i…