Takanori Nagamine

activity

20182026

collaborators

10 papers

math.AC2026

Quasi-factorially closed subalgebras of Laurent polynomial rings

Shinya Kumashiro, Takanori Nagamine

Let $R$ be a domain and $B = R [x_{1}^{\pm 1}, \dots, x_{n}^{\pm 1}]$ the Laurent polynomial ring over $R$ . In this paper we study pre-factorially closed (pfc) and quasi-factorially closed (…

math.AC2024

Remarks on retracts of polynomial rings in three variables in any characteristic

Hideo Kojima, Takanori Nagamine, Riko Sasagawa

Let $A$ be a retract of the polynomial ring in three variables over a field $k$ . It is known that if $char (k) = 0$ or $tr.deg_{k} A \neq = 2$ then $A$ is a polynomial…

math.AG2023

Affine and Unirational unique factorial domains with unmixed gradings

Gene Freudenburg, Takanori Nagamine

This paper studies the class of unique factorial domains $B$ over an algebraically closed field $k$ which are affine or unirational over $k$ and which admit an effective unmixed $\…

math.AC2023

Retracts of Laurent polynomial rings

Neena Gupta, Takanori Nagamine

Let $R$ be an integral domain and $B = R [x_{1}, \dots, x_{n}]$ be the polynomial ring. In this paper, we consider retracts of $B [1/ M]$ for a monomial $M$ . We show that (1) if $M=\prod_{i=…

math.AC2021

Generalizations of Samuel's criteria for a ring to be a unique factorization domain

Daniel Daigle, Gene Freudenburg, Takanori Nagamine

We give several criteria for a ring to be a UFD including generalizations of some criteria due to P. Samuel. These criteria are applied to construct, for any field k, (1) a Z-grade…

math.AG2019

Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units

Gene Freudenburg, Hideo Kojima, Takanori Nagamine

This paper considers the family $S_{0}$ of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field $k$ . Ou…

math.AG2019

Higher derivations of Jacobian type in positive characteristic

Takanori Nagamine

In this paper, we study higher derivations of Jacobian type in positive characteristic. We give a necessary and sufficient condition for $(n - 1)$ -tuples of polynomials to be extenda…

math.AG2018

Factorial rational varieties which admit or fail to admit an elliptic $G_{m}$ -action

Gene Freudenburg, Takanori Nagamine

Over a field $k$ , we study rational UFDs of finite transcendence degree $n$ over $k$ . We classify such UFDs $B$ when $n = 2$ , $k$ is algebraically closed, and $B$ admits a positive $…

math.AG2018

A note on retracts of polynomial rings in three variables

Takanori Nagamine

In Costa's paper published in 1977, he asks us whether every retract of $k^{[n]}$ is also the polynomial ring or not, where $k$ is a field. In this paper, we give an affirmative an…

math.AG2018

Closed polynomials and their applications for computations of kernels of monomial derivations

Chiaki Kitazawa, Hideo Kojima, Takanrori Nagamine

In this paper, we give some results on closed polynomials and factorially closed polynomial in $n$ variables. In particular, we give a characterization of factorially closed polyno…

Quasi-factorially closed subalgebras of Laurent polynomial rings

Remarks on retracts of polynomial rings in three variables in any characteristic

Affine and Unirational unique factorial domains with unmixed gradings

Retracts of Laurent polynomial rings

Generalizations of Samuel's criteria for a ring to be a unique factorization domain

Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units

Higher derivations of Jacobian type in positive characteristic

Factorial rational varieties which admit or fail to admit an elliptic Gm​-action

A note on retracts of polynomial rings in three variables

Closed polynomials and their applications for computations of kernels of monomial derivations

Factorial rational varieties which admit or fail to admit an elliptic $G_{m}$ -action