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VOL. 75 | 2017 Unipotent group actions on projective varieties
Rajendra V. Gurjar, Kayo Masuda, Masayoshi Miyanishi

Editor(s) Kayo Masuda, Takashi Kishimoto, Hideo Kojima, Masayoshi Miyanishi, Mikhail Zaidenberg

## Abstract

The correspondence between $G_a$-actions on affine varieties and locally nilpotent derivations of the coordinate algebras is generalized in the projective case to the correspondence between stratified $G_a$-actions on smooth projective varieties $V$ and regular vector fields on $V$ which are effectively locally nilpotent with stratification. These notions with stratifications are inspired by explicit computations of $G_a$-actions on the projective space $\mathbb{P}^n$ as well as the Hirzebruch surface $\mathbb{F}_n$ and the associated regular vector fields. Using partly these observations, we investigate the existence of $\mathbb{A}^1$-cylinders in Fano threefolds with rank one.

## Information

Published: 1 January 2017
First available in Project Euclid: 21 September 2018

zbMATH: 1396.14061
MathSciNet: MR3793364

Digital Object Identifier: 10.2969/aspm/07510119

Subjects:
Primary: 14R20
Secondary: 14J45