Affine threefolds admitting $G_a$-actions

R. V. Gurjar; M. Koras; M. Miyanishi; P. Russell

Affine threefolds admitting $G_a$-actions

Algebraic Geometry 2015-02-12 v2

Authors: R. V. Gurjar , M. Koras , M. Miyanishi , P. Russell

Abstract

Affine varieties of dimension greater than two can be explored their structures with the help of fibrations by the affine line or plane and quotient morphisms by $\mathbb{G}_a$ -actions. We consider $\mathbb{G}_a$ -actions on affine threefolds and discuss the structure and the singularities of the quotient surface as well as the singular fibers of the quotient morphism. Relative $\mathbb{G}_a$ and $\mathbb{G}_m$ -actions on $\mathbb{A}^4$ or on an affine 4-fold having $\mathbb{A}^3$ -fibrations over $\mathbb{A}^1$ are discussed when the actions leave one variable invariant or the fibration invariant.

Keywords

fibrations affine algebraic geometry algebraic group actions

Cite

@article{arxiv.1502.01849,
  title  = {Affine threefolds admitting $G_a$-actions},
  author = {R. V. Gurjar and M. Koras and M. Miyanishi and P. Russell},
  journal= {arXiv preprint arXiv:1502.01849},
  year   = {2015}
}

Comments

This paper has been withdrawn by the authors due to an error in the proof of Thm.3.1 which is not true in the present version

Affine threefolds admitting $G_a$-actions

Abstract

Keywords

Cite

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