Affine threefolds admitting $G_a$-actions
| Autor: | Gurjar, R. V., Koras, M., Miyanishi, M., Russell, P. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: This paper has been withdrawn by the authors due to an error in the proof of Thm.3.1 which is not true in the present version |
| Databáze: | arXiv |
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