Advanced Studies in Pure Mathematics

Unipotent group actions on projective varieties

Rajendra V. Gurjar, Kayo Masuda, and Masayoshi Miyanishi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 119-162

Dates
Received: 25 August 2014
Revised: 10 November 2015
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537498707

Digital Object Identifier
doi:10.2969/aspm/07510119

Mathematical Reviews number (MathSciNet)
MR3793364

Zentralblatt MATH identifier
1396.14061

Subjects
Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30]
Secondary: 14J45: Fano varieties

Keywords
regular vector field unipotent group stratified $G_a$-action Fano variety

Citation

Gurjar, Rajendra V.; Masuda, Kayo; Miyanishi, Masayoshi. Unipotent group actions on projective varieties. Algebraic Varieties and Automorphism Groups, 119--162, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510119. https://projecteuclid.org/euclid.aspm/1537498707


Export citation