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

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5 papers · 1 filter

math.AG2026

Nagata's conjecture on a polynomial automorphism in positive characteristic

Shigeru Kuroda

An automorphism of the polynomial ring $k [x_{1}, \dots, x_{n}]$ over a field $k$ is said to be $tame$ if it can be obtained by composing affine automorphisms and elementary au…

math.AG2024

On exponentiality of automorphisms of $A^{n}$ of order $p$ in characteristic $p > 0$

Shigeru Kuroda

Let $X$ be an integral affine scheme of characteristic $p > 0$ , and $σ$ a non-identity automorphism of $X$ . If $σ$ is $exponential$ , i.e., induced from a $G_{a}$ -action…

math.AG2020

Linearization of holomorphic families of algebraic automorphisms of the affine plane

Shigeru Kuroda, Frank Kutzschebauch, Tomasz Pełka

Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $C^{2}$ , holomorphically parametrized by an open Riemann surface, is linearizable. As an…

math.AG2015★ 6 cited

Cable algebras and rings of $G_{a}$ -invariants

Gene Freudenburg, Shigeru Kuroda

For a field $k$ , the ring of invariants of an action of the unipotent $k$ -group $G_{a}$ on an affine $k$ -variety is quasi-affine, but not generally affine. Cable algebras are introdu…

math.AG2014

Degeneration of tame automorphisms of a polynomial ring

Shigeru Kuroda

Recently, Edo-Poloni constructed a family of tame automorphisms of a polynomial ring in three variables which degenerates to a wild automorphism. In this note, we generalize the ex…

Nagata's conjecture on a polynomial automorphism in positive characteristic

On exponentiality of automorphisms of An of order p in characteristic p>0

Linearization of holomorphic families of algebraic automorphisms of the affine plane

Cable algebras and rings of Ga​-invariants

Degeneration of tame automorphisms of a polynomial ring

On exponentiality of automorphisms of $A^{n}$ of order $p$ in characteristic $p > 0$

Cable algebras and rings of $G_{a}$ -invariants