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Configuration spaces of the affine line and their automorphism groups

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Zaidenberg,  Mikhail
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1505.06927.pdf
(Preprint), 698KB

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Citation

Lin, V., & Zaidenberg, M. (2014). Configuration spaces of the affine line and their automorphism groups. In I. Cheltsov (Ed.), Automorphisms in birational and affine geometry (pp. 431-467). Cham: Springer.


Cite as: https://hdl.handle.net/21.11116/0000-0004-DB89-B
Abstract
The configuration space $\mathcal{C}^n(X)$ of an algebraic curve $X$ is the algebraic variety consisting of all $n$-point subsets $Q\subset X$. We describe the automorphisms of $\mathcal{C}^n(\mathbb{C})$, deduce that the (infinite dimensional) group Aut$\,\mathcal{C}^n(\mathbb{C})$ is solvable, and obtain an analog of the Mostow decomposition in this group. The Lie algebra and the Makar-Limanov invariant of \mathcal{C}^n(\mathbb{C})$ are also computed. We obtain similar results for the level hypersurfaces of the discriminant,
including its singular zero level.