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arXiv · 1502.01849

Affine threefolds admitting $G_a$-actions

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

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R. V. Gurjar, M. Koras, M. Miyanishi, P. Russell. 2015-02-11. Affine threefolds admitting $G_a$-actions. https://arxiv.org/abs/1502.01849

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